It depends. Money in a regular savings is considered an asset on both the FAFSA and the Profile.
The FAFSA doesn’t consider home equity in your primary residence…at all. SOME colleges that use the CSS Profile do consider primary home equity.
Im going to give you some very free advice that really comes from @blossom who can clarify. Do NOT do anything financially that you wouldn’t be doing anyway. IOW…don’t buy a house or primary residence just because you think it might help with financial aid.
The vast majority of colleges do NOT use the CSS Profile…so your primary residence equity won’t matter. And the very vast majority of colleges do not meet full need for all students. You could do financial gymnastics that won’t net you a dime of additional need based aid.