Not following you here: Your suggestion for evidence that 3rd party batteries will be available is that some guy in Finland couldn't get enough supply?
A single hobbyist in Finland could run a profitable business replacing Nissan Leaf batteries unofficially. The dude managed to install a 25% larger battery in the car and fool the on board computer to accept it.
Just imagine what can be done with actual resources and R&D.
The current limiting issue isn't skill or technology, but available new batteries. They can't make them fast enough even for new cars, never mind for spare parts.
But when battery production ramps high enough, there's absolutely nothing preventing people from upgrading existing batteries with more modern tech - bigger battery capacity in the same space.
There will also be a huge industry converting "dead" EV batteries to in-house battery backups. A car with 50% battery degradation is a bit iffy, but the battery will still have tens of kWh of usable capacity. Enough to run a house for a day or two in a pinch - or just store cheap energy and sell it back to the grid when the price goes up.