Late 2013 RMBP switches to SCO(very poor quality) codec when using earbuds microphone It switches back to AAC once I pick the internal microphone as an input.
Does this mean that the bluetooth version is too old to handle both audio input and output with the earbuds? If so, can a bluetooth 5.0 replacement for the network card be purchased somewhere?
Based on the system report, my current bluetooth is 4.0 (0x6).
The earbuds are Samsung Galaxy Buds+
They work nicely on my iPhone X.
None of this will work.

The Samsung Galaxy Buds+ require Bluetooth 5.0
The 2013 MacBook Pro's AirPort adapter Bluetooth is 4.0 and was a nice, industry standard PCIe slot so you could swap it out for another
The next Mac with Bluetooth 5.0 is the 2018.  Unfortunately, it doesn't use the old &quot;tried and true&quot; Broadcom chipset - it uses a proprietary Apple/USI (Universal Scientific Industrial) Bluetooth module.  So, the question becomes, even if you could source a BT 5.0 module from a different vendor - where are you getting the drivers?

What bugs be about Apple is this need to be so rediciliously proprietary that upgrade-ablity concept has been literally thrown out the window.  Like you asked...

If so, can a Bluetooth 5.0 replacement for the network card be purchased somewhere?

The answer should be yes.  You should be able to get a PCIe WiFi/BT card from a different manufacturer like Dell or HP (or even Apple themselves) and upgrade it for additional features.  However, Apple immediately puts a stop to that by tweaking the AirPort card's firmware so that only its drivers will work.
If the 2018 MacBook Pro had continued to use the PCIe slots instead of soldering to the board, you could have theoretically swapped out the AirPort cards from one to the next and still have all the native Apple drivers.  Unfortunately, you can't.
Your solutions are limited:

Get BT 4.0 headset/earbuds specifically for you Mac
Upgrade your Mac
Try an external BT dongle (not recommended)

Apple has traditionally not played nicely with more than one BT dongle attached so I would avoid.  You can try - it won't break anything (physically) but macOS probably won't appreciate having two BT devices and you could break some functionality.