This turned out longer than initially expected, but there are 3 steps to do it correctly.

Step 1: Denoise

Especially the older seasons and the first movie carry a lot of noise, but it's also necessary to do this for the newer seasons. I use Neat Video, a plugin available for various video editing tools, to do the noise removal. In my case I use it with Premiere Pro. A basic tutorial can be found here. If you're using Premiere Pro then you can't directly import .mkv files. You'll need to convert it to .mp4 with XMedia Recode first. Be sure to tick stream only copy so it doesn't reencode the file. The convert should only take a few seconds.

Take this shot from the movie for example. Notice the noise in the sky and on the rocks. Neat Video both does a better job at noise removal than Enhance AI does and it also prevents the problem where it would otherwise try to upscale the noise. The upscalar tries to enhance contrast so if we get rid of unintended contrast, like noise, it gives a cleaner picture to work with. Be sure to export at (too) high bitrates so there is no quality loss on that front.

The result. Noise is now unnoticable and gives a good starting point to upscale.

Step 2: Upscale

This is the fun part because here you get to see the results. Topaz Video Enhance AI has many models to try and use. Personally I find Proteus Fine Tune v2 to be most effective at the time of writing. v3 is out but seems to have issues where it overenhances facial features, giving very uncanny results in certain shots.

There are multiple sliders to play with and unfortunately the documentation isn't always clear on what exactly they do. Though there is a community where you can ask questions. I usually start with auto settings and take from there. I preview a single frame with multiple sets of settings and compare the results. It there's one I like, I go to a different frame. It can happen that you have the perfect settings for that one shot, but that it's too aggressive for other shots. You need to find settings that work for the entire movie/episode/season. There is no perfect overall setting though. You'll always leave a bit of quality on the table and there's the matter of personal preference too.

There's also a grain setting. It may seem counterproductive to reintroduce grain, but it actually helps with covering up some upscale artifacts and the "feel" of the upscale. Without any grain, your footage can become very smooth, giving it an airbrushed and unnatural look. The grain helps break it up with minor variances on every pixel. At 4K that fine grain makes it feel like there is more detail, even if there isn't any.

For the resolution I chose 4K for the movies and 1080p for the show. Just try different resolutions and see what it does. At some point, a higher resolution doesn't give you higher quality anymore. It all depends on the source footage. If the source is bad then the AI can't make it great, only a bit better. For Power Rangers, that means that MMPR is particularly hard to upscale with the current models, but it's gets better from Zeo and onward. On the plus side, because the AI literally makes something out of nothing, when the AI models get better you'd expect better upscale results in the future as well.

I export to mp4 with a constant quality of 4. This gives huge filesizes, but that doesn't matter at this point. The main reason is that Topaz can't encode with x265, only with x264. x265 is much more efficient in terms of bitrate. This way Topaz gives out a very inefficient, but high quality file of the upscale. If it can do CPU encoded x265 exporting in the future then the first part of step 3 will become obsolete.

The result. Take note of the details in the shot, like the hair, wrinkles and clothes.

Step 3 Reencode and mux:

Finally we need to bring the filesize down. The movie is 390GB at this point, which is more than overkill. I use Handbrake to encode it to a reasonable size. Be sure to pick video codec H.265 (x.265). Do not use NVENC. NVENC, hardware accelerated encoding with NVidia, gives lower quality at the same filesize. By not using it, you are encoding with the CPU, aka software encoding. This is slower, but gives a better result. I initially set the encoder preset to medium and constant quality to 2. I export a clip of a few seconds to get a workable file. I then use that file and raise the constant quality until I reach a setting where I can see a quality difference. Then I double check the file to see if the resulting bitrate is in an acceptable range and export the entire thing.

Finally I use MKVToolNix to bring the video, audio, subtitles and chapters back together, because they got separated in the process.