Preference.
Pressing any fruit extracts more liquid, but with that comes harsher elements, so it's a trade off.
A lot of folks prefer "free run" wine, e.g., wine that requires no or little pressing. That makes sense, as the wine has the least harshest elements.
OTOH, my 2020 wines are a Merlot/Bordeaux Blend which was 100% free-run wine, and a Merlot/Zinfandel/Bordeaux Blend that included the pressings from the Merlot and Bordeaux Blend, and all (free run + pressings) of the Zinfandel.
Folks prefer the second wine over the first.
If you're looking for help in decision making, I realize I'm not being anything close to helpful!
I suggest you use light pressure on the bag, and segregate that wine. Then press the bag hard, and likewise segregate that wine. Waste not, want not.
Use the pressed wine on a case-by-case basis. Adding some or all into the free run wine may make it better. If you're low on top up, well, it may be necessary to use it.
If the pressings are too harsh, it still makes good cooking wine. Keep your options open.