So I've made a solution that works for myself. I believe all but one part should be generally useful.

First off, I found Piwigo Import Tree when I was 95% done with this. I'm not using it in part as I was basically done with my solution, and there were some gaps in the documentation that left me wondering if it was a good fit for my flow. But it might work for you, so check it out.

As for my solution, in short I make a text file list of all the videos I want to upload, and then process these files with fileProc, a Python script I made to run a set of commands on a set of files. I have it configured to:
1. Transcode a video to a level a quality I've found to be a good balance of size and quality with HandBrake-CLI.
2. Generate a poster image with ffmpeg.
3. sftp the directory structure to my server. I have a public/private ssh key in use, so no login is required.
4. Use piwigo-actions, another set of scripts I made, to login to piwigo, run synchronization, and log out. I also found piwigo-scripts which does the same and more. But I believe it is intended for older piwigo sites as the URLs used don't match what my site uses.
5. Clean-up my local directory as I don't care to have backups of the files.

I have more thorough documentation on the sites for each tool, but there are a few points worth calling out here:
1. fileProc is hard coded assuming you want to use my file structure. Photos are organized by date locally in folders of yyyy/mm/dd. And you want them in folders on piwigo like yyyy/mm_Month. I'd like to make this more generic so others can translate their folder structure however they want, but currently you'd need to modify the code to handle something else.
2. I've tested this only on my linux machine. I suspect on Windows or Mac you'd have trouble getting them to work. The key dependencies are bash and curl for piwigo-actions and python3 for fileProc. But all the configured commands I run to do everything else within fileProc also assume bash and other unix commands.
3. This ends up with the videos available on your site, but they are missing checksums. I'd like to make this automatic. But should probably just write a bug report (if I can ever access the bug site) as it seems like a deficiency in Piwigo's synchronization.

Hopefully this is helpful. I'll do what I can to answer questions. Unfortunately, I probably won't have much time to improve the tools in the short term. Though the hard coded assumptions on directory structures is really bugging me.

Hi blacksmith,
piwigo-actions/piwigo.sync.sh is the same doing a Synchronize action through your piwigo website. So it doesn't do much without the other actions and something to tie them together, like my fileProc script. I haven't tried tools/remote_sync.pl, or found documentation for it, so I don't know all the ways they may differ.

I should add I haven't tested my tools with Piwigo 11, so they may be broken. I'm waiting on key extensions to support it, or a chance to test it out myself. But don't have a lot of time for it, so it may be a while before I upgrade.