Keeping a 2006 Giant SCR 3 on the road - 9 speed to 11 speed?
I think your minimum refurb to bring the bike up to a good standard would be: new wheels; bottom bracket, chain, cassette and chain-rings; housings and cables (shift and brake); tires, brake pads, bar-tape; and a total, thorough cleaning and re-adjustment. This is assuming the derailleurs and shifters are actually working OK, and your LBS just means 'obsolete' when they say they are at 'end of life'.

That's a fairly big chunk of the bike, so you may want to go the whole way and upgrade the groupset. Personally I'd want at least 10 speed as an upgrade - Current Tiagra 4700 is 10 speed. Another option is looking for lightly used 105 5800 or Ultegra 6800 (or perhaps even R7000 or R8000) 11 speed components.

I'd look for a good set of lightly used wheels. As tech has moved to disc brakes and thru-axles you can probably find some really good light and strong rim/QR wheels for reasonable money.