2015 Macbook Air shuts down with 75% battery power remaining?

This has been a problem for the last 3 months. First time I noticed was when I was running on battery power and suddenly the computer shut down with Battery status around 45%. After plugging back in and charging to full I noticed (for the first time) that even though battery showed 100% the battery icon still shows charging and never shows the fully charged icon. Says: "Service Recommended”. Now computer running on battery will automatically shut down around 80%(!).

Charge Information: Cycle Count: 248 / Charge Remaining: 4088 / Fully Charged: Yes / Charging: No / Full Charge Capacity: 4209 /

I've also run the Coconut Battery program and it states Device Age: 39 months / Health: 59% / Cycles: 248

I've tried re-setting SMC (a few times). I've tried re-calibrating the battery also with no success.

I've run Apple Diagnostics a few times over this period as well and says everytime: NO issues found. Ref Code: ADP000. ----- In other words.... No battery issues which would have been codes: PPT004, PPT006, PPT007. Very weird imo.

Does my Macbook Air actually need a new battery or is there some other problem that I have not yet figured out? Cost of battery here in Canada is $169 here on Apple's site, but authorized dealers have quoted me from $269 to $320 to do it. That's why I'm hesitant. Apple stores themselves have not yet re-opened from COVID-19 shutdowns.

Any help or new suggestions for testing would be appreciated.