I always set the output framerate as “Same as source”, and when I do that the only options change from CBR & this other one I can’t remember to CBR & VBR. When it does this, it defaults to VBR. Should I change it to CBR instead?

Do you mean Constant Framerate and Variable Framerate? Because CBR and VBR mean Constant/Variable Bitrate. Anyway, I always set my stuff to same as source as well, with a constant frame rate. I don't think this really matters because the video you are feeding to Handbrake is itself probably constant framerate, and therefore the result ends up being constant frame rate even with the variable frame rate option.

as far as I know MKVs tend to have smaller file sizes typically than MP4s for the same media

This is not correct. MKV and MP4 are just container formats. The stuff that actually makes up the size is what goes into those containers (the video stream, audio stream, and to a much lesser extent the subtitle files, chapter markers, and any other metadata).

I’ve read that mkv is more tuned for backups of TV shows & movies, and mp4 is more tuned for backups of web content (due to the streaming thing you mentioned)

MKV is an unbounded container. You can pretty much stuff anything into it, which is why it's used for archiving. MP4 technically isn't limited to its normal expected codecs through some clever use of metadata, but it is basically unexpected and mostly unsupported. It's certainly unconventional to use it like how you would use an MKV.

mkv is both an open format and libre, unlike mp4 which is only the former

This is true, but not realistically relevant. Mp4 is old. I don't know if it still has patents but judging by the date it was defined I would have to believe most if not all of its patents are expired. Though I am just guessing at that. But even then, that's not important because basically everything plays mp4s because its open format is implementable by anyone. Given everything you've said, though, I agree that MKV is probably the better format to use.

I mainly see my backups first and foremost in an archival light

Then you should not use Handbrake, unless you plan to keep two copies of your media. MakeMKV should remux the blu ray discs directly into MKVs (I've never used it to do blu rays, but I have used it with DVDs to do this job). If you do anything to your media with Handbrake, it's not really an archive anymore, it's just a good copy. For many people this tradeoff is worthwhile because if you encode it at high enough settings you won't get any visual loss but you will get a much smaller and more easily manageable file. But I would only call it an archive if it's untouched from the source. That's what the term "remux" implies: Taking the original video/audio stream contents and putting them into a new container such as MKV.

As an aside comment, I don't understand how the term remux came into use, since a multiplexer selects a single signal among multiple...