How much does a MacBook Pro Logic Board replacement typically cost?

Only you can decide if it is worth repairing versus the cost to purchase a new laptop. Usually if the repair costs less than 50% of the price of a new laptop, then it is generally Ok to repair it. But if the repair cost is around 50% of a new laptop, then it is literally a coin toss. If the repair cost is significantly more than 50% of a new laptop, then I would go for the new laptop. However, personal circumstances & needs can play a part in the decision as well.

Keep in mind this will be a repaired laptop which suffered storm damage. Did Apple catch all the bad parts? Did the tech do a good job working on & reassembling the laptop? These are all risks of a repair option. Liquid damage can be tricky since it may not always be obvious if a part may have hidden damage, it may not even be noticeable right away in system behavior or performance. With these newer models, there are very few individual parts anymore....in fact there are just a few major component part assemblies which Apple replaces (Display, Logic Board, Top Case/Keyboard/Battery Assembly, Trackpad). There are only a few small components remaining (I/O Boards, Antenna Board, Audio Board, Speakers).

I guess it also depends on whether you are going to claim it on your insurance. If so, then your insurance may have a say in which option you can choose.

All Apple laptop repairs are expensive with these recent models even if no accidental damage is involved. I'm guessing Apple is quoting you a price from their Accidental Damage Tier associated with a mail-in repair which is based on the most expensive component(s) that are damaged. Apple does tend to replace a lot of parts on those mail-in repairs. I've seen Apple sometimes replace just about every component on the damaged laptop which surprise me.

I'm not sure if this helps, but it does give you some things to consider in making your decision.

I wish you and your family well and hope the recovery goes quickly & smoothly.