Should I use all my “profit” from home sale as down payment on new home?

This situation is still hypothetical at the moment as we haven’t decided if we’re going to do the move yet.

I may be moving to Virginia from New York in order to take care of my parents. This would result in a massive pay cut (although probably better qol). Currently I make around $300k with overtime. In VA I would be making about $120k (no chance of ot but I’m not complaining). Based on comps in my area, I have about 250-300k (maybe even more but don’t want to be too optimistic) in equity in my house. The homes we have looked at in VA around $400-550k. Would it be smarter to use all that equity as a down payment on a house in VA or to set some aside as investments or into my 2 yr olds 529? I can even get a 0 down VA loan if I wanted to but probably wouldn’t be able to afford that mortgage with the new salary. I would like to keep my mortgage payment as low as possible but certainly recognize i may be better off using some of that money elsewhere to work for me, but I’m just not really knowledgeable enough about that stuff to decide which is better or how to use it.

Aside from my current mortgage our only debt is 2 car notes totalling $1k/month. If it matters I max out my TSP and will have a pension of about $80-90k/yr after I retire at age 56 (mandatory retirement age in my job).