You've earned the days as paid vacation, you don't have to work during them. The money it costs to pay you for those days is part of your compensation for the work you've already done and the stretches of time that you came to work instead of taking the day off.
If you do decide to take the time to work on finishing up some papers, that could be good for both your advisor and you. All your work is basically a waste of time if it never makes it into a paper. Maybe you're fine with that if you're all done with academia, but if you ever did want to return then any papers you can publish will be to your benefit. I think there's also a strong sense of personal accomplishment in publishing papers (why are you doing research if not to share it with the research community??), and as a post doc (or any other level of academia) your role is a bit different from a standard employee in that you're typically doing research not just as a job but as your personal work.
As far as "not being able to afford" to pay for those days, I think you can mostly ignore that statement, it's not connected to what you do next in any real way. However, it's probably not motivated by your advisor literally being that broke, but rather that they expected that the grant money they spent on your position would result in some output that they can use to get more money for future projects - that's how the academic funding cycle works. If they've paid you for a spot and you've failed to complete projects, that's in many ways wasted money for them. Maybe they can pick up your work where you left off but often there is a lot of cost of time and effort in starting from someone else's partial work.
I won't comment on legal issues according to any letter of the law, but it's extraordinarily unlikely that you would see any legal consequences for spending time off working to complete a project. It's also unlikely your advisor would see any consequences for making the request. It also doesn't seem that your advisor is seeking to cause you to lose out on any money but rather they're hoping that you see enough value in completing work to spend your earned vacation time working. Like I said in the start, you've already earned this time and don't need to work for it, but it's a bit different from trying to pull money out of your pockets.
@GoodDeeds in a comment pointed out that OP's advisor may be asking them to "quit early" and count the end of their work as vacation time. I was thinking more along the lines of OP determining their own end date but their advisor asking that they keep working to finish up projects. Also in a comment, OP indicates that they are willing to work to finish up the incomplete papers on their own time.
Based on those pieces of information, my advice would be to:
A) Assure the advisor that you are willing and intending to finish up these projects. I think that's their main concern, whatever conflicts there have been between you. Everything you've said in this post could be a completely honest, non-exploitative effort towards this goal. Maybe that's overly charitable towards them, but I think it's a good mindset to start from.
B) Come to agreement on an official end date, when your regular salary ends. You should be committed to work full time through this date, like you've been doing until now. This shouldn't have any relation to the vacation hours you are owed. Pretend they don't exist. After that date, you're committing to finishing the projects, but not to working any set hours. If your advisor wants this to be sooner, you can say that if you aren't an employee during those hours there are other things you'd like to do during that time.
C) If your advisor insists on involving the vacation hour pay, reiterate your commitment to finishing up the work. If it helps your advisor to think about it, those volunteer hours you plan to put in on these projects in your nights and weekends are effectively "working for those vacation hours", you're just not willing to have those be "full time" hours on a schedule, or to substitute for your normal work.
If they aren't okay with this arrangement, then they aren't being reasonable. You can hope they come around, but remember that you have some power here. Your advisor is going to want you to finish your projects. You have a new job and aren't compelled to work for them. So, if these papers are going to actually get out, the two of you have to work on mutually acceptable terms. Good luck!