Piracy: ꜱᴀɪʟ ᴛʜᴇ ʜɪɢʜ ꜱᴇᴀꜱ

How much RAM do you need for Topaz? I have access to a 2080 ti 11GB and a 6900 XT, but both systems only have 16GB of RAM.

Before I built this machine, I had 32gb of RAM. You should be fine with 16gb as it isn't that RAM heavy. Just close out anything not Topaz. Topaz is going to 100% your machine (like it does mine) anyways so you do not need anything else up. On that note, I recommend upscaling over night. A 1080p-4k upscale can easily take my machine 7-11 hours to do. You shouldn't have that long since you are only trying to bring something to 1080p, but still be aware your computer may be occupied for a couple of hours.

Are there any specific profiles for Topaz you can share? (I assume it supports something like that?)

Yes there are profiles, but they are better for keeping things persistent between series (like I have a Sabrina profile just for Sabrina) rather than a one size fit all. I do have one I found to upscale BRs to 4k with only slight adjustments. I will post in a follow up comment once I get off work. In general though you want to make slight adjustments, render a few seconds of video, review it, then make more adjustments. When you like it, apply that to different scenes in the same movie (I recommend testing dark/night scenes for sure since those a tricky for AI) to make sure it works, then do the actual upscale.

I will also throw in my Sabrina preset since I managed to use it to upscale some other DvDs with minor tweaking as well. It should provide a good starting place for your DvDs.

Is there something equivalent to Topaz on Linux?

I do not know Linux, sorry :(

The amount of commercial AI upscaling software is rather limited (at least when I started searching this May) and focused towards a Windows and maybe Mac audience. That being said, I know there are AI upscaling software on Github so I would not be surprised if someone ported something like Waifu2x (an open source AI trained to upscale anime) to Linux. As to their quality, I do not know. All I can vouch for is that of the commercial software, Topaz was the best when I bought it in June.

How do I get a DVDRip to look clean without any further compression? By default MakeMKV results in files with these annoying lines, which only disappear after passing it through Handbrake (deinterlace/decomb).

I do have a program to deinterlace (remove the annoying lines) which I will also provide you the name of when I give you my profiles. Topaz can also do decent deinterlacing, but my program is better (and also free).

Will I have better results only upscaling to 720p or does the output resolution not matter in terms of AI artifacts?

It is going to depend on how clear your source is. If your input has a lot of compression artifacts, then that means more guesswork for the AI, and more chances for Topaz to guess wrong. Upscaling to 720p is going to be a lot more successful in general since its borderline HD, but if you have a good source and don't mind the occasional weirdness really only noticeable if you know what to look for, then 1080p is doable for even something like 360p.

One thing I like to do (to the anger of many film purists) is add my own film grain in post. There is something about film grain that helps our brains not notice small errors in the upscaling process. Holy Grain is a very good film grain in 1080 and 4k. Sadly I never found a torrent of it so I ended up spending the cash to buy it myself.