MacBook Pro will only charge if using a 3rd party adapter after battery replacement
If you have two genuine Apple MagSafe chargers and neither with charge/power you MacBook Pro, but a knockoff charger will, there’s an issue with your MacBook.  More than likely, it’s the DC-In board.
How it works.
In the genuine charger, there’s a chip in the MagSafe connector (not the “brick” but the magnetic part with the green/amber LED) that identifies the charger to your Mac.  If the wattage advertised is greater than or equal to what’s required, it’ll charge.  If not, it won’t and if your computer is on, will even notify you that the wrong charger is attatched.
The way it charges is that the circuitry in the DC-In board detects power from the adapter from the presence of current on the one wire charging circuit.
So, if it’s charging with the knock-offs but not the OEMs, it’s bypassing the wattage check and just “dumping” power into the DC-In board.  You don’t want this, because this is how things get fried.  Why aren’t the knock offs using the identifying chip?  Most likely cost.
The fix is simple: you need a new DC-In board.  See this related answer for more details.  It’s also called an I/O board because some models have I/O ports on it; this one doesn’t. Note: it’s possible that there may be damage to the charging circuitry on the logic board, but without putting hands on, it’s impossible to know.
A few clarifications

The 2012 13” MacBook Pro models require the 60W power adapter
Keep/use the 85W charger as it’s perfectly safe to use a charger with a higher wattage rating than what’s required
Your battery is not really related to charger wattage.  The only thing that will happen is your charging speeds will differ.  The wattage requirement is based on both charging and compute requirements (what it takes to drive the computer).
Only use genuine Apple chargers with your Mac.  Cheap knock offs can end up costing you more!
The last Mac with the MagSafe adapter was the 2017 MacBook Air which was discontinued in 2019.  The chargers will be around for a while longer.  See Apple’s Vintage and obsolete product page for a list of currently supported products.