Agree with the coach but if you're planning on buying new clubs, then yes, get a fitting from a true Titleist fitter at an outdoor range. Some golfers are naturals who can play well with any clubs, and some (like me) have to work at it their entire life. My first iron fitting was 7 or 8 years ago and it led me to the realization that for us who are always working on our swing, fitted clubs seem to be more beneficial than to those with that natural swing. If you can find a Titleist fitting, you have nothing to lose (there is no commitment or pressure to buy).

Not sure of your age or club heads speed, or how much you intend to play going forward. Yes, you do need to correct the swing fault(s) that cause fat/thin shots. Or at least minimize them.
New irons will provide some help on mishits. The T400’s provide the most support for mid to high handicappers with driver head speeds under 95. You should be able to negotiate with a fitter when the learning curve will intersect with the advantage of newer technology. If the current irons do not match well with your ability, they may be contributing to some of your difficulties. New clubs will not drop your handicap by 10 strokes but they may make the game more fun. Whether T300 or T400 clubs will be best for you can only be determined by a proper fitting. Your personal improvement will depend on how often you practice or play.

I agree with your coach, he has given you some good advice. Hopefully you have completed your physical therapy and your muscles are strong enough to resume golf. Rushing back in could make things even worse. Work with him on that game until you get your swing back, then consider going to see a certified fitter. Most Titleist certified fitters do charge a fee and in some cases the fees are applied towards the purchase of the clubs. The fitter will steer you in the right direction regarding club selection and shaft. Hopefully you will choose Titleist clubs. New clubs should be available to the public this fall and I would wait until they are released to get the most up to date technology. Good luck with your return and sounds like you have a very good coach. I am 75 and listened to mine after back surgery.

Getting the new clubs and getting fitted for them cannot do you any harm.

Yes

When the time comes for you to get a new set of clubs, getting fit is a must. Buying a set of golf clubs off the rack or ordering online, sight unseen is like flushing your money down the toilet.

Definitely get fitted. I work at a pro shop and fit athletes all the time. Easily worth it especially if you’re investing time into the game.