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I would certainly choose slivers over filler for those gaps. There's no way filler will stay in those. You can get random size slivers so you can mix it up. Sometimes you might just get a couple of mm in a tiny gap other times you might need to wedge two in together. Some times you might need to snap s length in half and go down to a smaller size as the length changes size. It's pretty simple to work out how to do it but like I say it's back braking work. Think I spent 4 days on our old small dinning room...
To me it looks like you need to spend time scraping out the gaps. Circular saw may help. Them slivers. Then chisel off anything proud. Then sand.
I'd say you've got a lot of work ahead of you but the end result could be a very impressive looking floor.
Completely doable within the inexperienced DIY skill level but like I said it's back breaking. I did mine in my mid 20s and in my late 30s it would certainly take a toll now.