Puppys operate under the principal "If it ain't broke, don't fix it."
You'll notice some Puppys fans are happy to use Puppys several years old. You, in fact, are running bionicpup32 which is 'binary compatible' with Ubuntu Bionic Beaver. The latter was released in April of 2018, more than 3 years ago. Puppy Package Manager has access to the Ubuntu Bionic Beaver repositories, including its Updates and Backports repositories. You can at any time run Menu>Setup>Puppy Package Manager, Click the Configuration tool on the Top-Left, 3rd from the Left and update its databases. In fact, its recommended that you do so before attempting to install anything via PPM. But, what exactly do you hope to find which wasn't fixed two years ago?
There are two and a half good reasons to 'update': (1 and 1 1/2) Web-security and web-media demands; and (2) You need the latest 'Bells & Whistles' on some application that didn't exist at the time the then current version for your OS was published.
Newer isn't always better, especially if you trying to get work done with less than the newest computer. Newer applications are created to take advantage of the computing resources --more RAM and more powerful CPUs-- of those computers. Such greater resources can handle the more larger/demanding applications. A computer with fewer resources, if t can handle the newer version at all, will have to struggle and appear less responsive.
One example I'm very familiar with is LibreOffice. I haven't changed how I use it over the last 10 years. They haven't added anything I need since the 3 Series. I could still use a 3-series Suite in even the newest 32-bit Puppy. I use the 6-series because --although it take up much more disk-space-- they actually developed a technique for more efficiently using RAM. But for several years, when what was being published were the 4 and 5 Series, for my needs they were just larger and slower.
Four years ago, shinobar published gimp-portable version 2.8.16.0.5, having some improvement over the version he had published 2 years earlier. http://shinobar.server-on.net/puppy/opt/pup5/ . Both are about 17 Mbs and will work well under bionicpup32. I don't have a recent 32-bit Gimp SFS or AppImage. But a recent 64-bit SFS is 51 Mbs and a recent AppImage is 161 Mbs. Neither offers anything I use which Shinobar's publications didn't provide. And, in fact, the new AppImage made changes I don't like.
Ubuntu no longer publishes 32-bit operating systems. To create 32-bit ‘ubuntus’ newer than Bionicpup, peebee and 666philb have had to use some binaries from debian. debian still publishes 32-bit operating systems; and josejp2424 publishes 32-bit Puppys built only from debian binaries. If you need an application newer than those on Ubuntu’s Bionic Beaver's repos, you’re very likely better off running one of the operating systems to which I’ve just referred than trying to hobble-together an application for bionicpup32 employing the applications found on repositories for the newer operating systems. Trying to do the latter involves searching for the applications, themselves, the libraries they require, the libraries those libraries require, creating symbolic links so that your old system will use the newer files, stitching them all together; and the product you’ll have after hours of work still may not function.
The Web, however, presents an entirely different condition. Websites are driven by two factors: (1) preventing malware from damaging the websites and (2) providing those who access the website with the most feature-rich graphics and media. It’s an up-ward cycle requiring more complicated structures and demanding more computer resources, each feeding off the possibilities of the other. As websites change to meet those conditions, older web-browsers are no longer allowed access. Consequently, web-browsers must keep pace.
6 years ago, firefox was an 18 Mb download; today 71 Mbs. 5 years ago, Google-Chrome could be published as a 65 Mb SFS. Today, the easiest way to publish it is as a 125 Mb portable. In fact, there isn’t even a 32-bit version of Google-Chrome. Google stopped building for that architecture 2 years ago. But there are current 32-bit slimjets and vivaldis built from chromium (google-chrome’s ‘test-bed’). The portable builds for them are 104 Mbs and 151 Mbs respectively. Portables are downloaded as compressed tar.gz files. When decompressed to storage, they require 2 to 3 times the amount of space as the tar.gz. But the same is true of pets and SFSes. 5 years ago you were fortunate if you had more than 50 Gbs of storage space. Today we think in terms of terabytes. A couple hundred megabytes of storage is meaningless. But on an old computer, several hundred megabytes of RAM may still be significant.
One of Puppy’s objectives is to enable the owners of older computers, if possible, to avoid replacing them except by choice. Several Puppy ‘fans’ undertake the hard-work of building newer versions of applications and publishing them. You’ll find such applications on the “Additional Software” Sub-Forum, viewforum.php?f=7. Some are published as pets you have to install. But to a large extent Web-browsers are published as SFS or portables; and references are provided to AppImages for 64-bit operating systems. You’ll find them here, viewforum.php?f=90. These packaging formats are particularly appropriate for Web-browsers as they are NOT installed. Rather, you just download and use them via their respective techniques. That enables you to try a new version without discarding your old; then choose whichever works best under your system. Upgrades are as frequent as circumstances permit. It pays to check that Section often to see what may now be available for your Puppy. However, if you are using firefox or palemoon, these have builtin mechanisms for updating.
If you're particularly concerned with ‘security’ there’s one other easy upgrade you can do with Puppys published in the last 6 or so years. You can replace its kernel with a newer version in less than 5 minutes. Newer kernels are compiled to include patches against some then known potential malware. However, newer kernels may not include the drivers and firmware required by your computer. Still, it doesn’t take long to create another folder, copy files into it; configure your boot-menu to offer a 2nd frugal Puppy and boot into it to see if there’s a mismatch; then keep either or both moving/copying your SaveFile/Folder as may be appropriate.
There’s one other theoretical upgrade to security modules One of the security protocols which all web-browsers use is openssl. Newer openssl packages are a simple download & install. However, they depend on newer glibc libraries. An operating system can only have one built-in glibc library, and that glibc is used by all the builtin applications included in your Puppy version. A newer builtin glibc library would break those builtin packages. That circumstance is one of the reasons ‘rolling distros’ roll, and other major distros publish new versions. Puppy Devs are investigating possible work-arounds. But currently none are available.
But before you rush out to replace your Puppy, keep in mind (a) its current openssl is probably not being rejected by websites; and (b) with over a million posts to this and the old forum, no one ever reported actually having been effected by malware. That, in part, may be a result of how in operation Frugal Puppys function differently than other Linux Distros.
If you want something more like apt, install pkg-cli, https://oldforum.puppylinux.com/viewtop ... 71#p985531 if it isn't already built into Bionicpup32. It may be on its Setup Submenu. The above thread will explain how to use it. Like apt, it enables you to easily link to other repos and install their packages. [Not that doing so might not break things. 
You really still need to know what you are doing.]
