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I had years of coaching when I was young so a lot of it is in my brain, I just need to remember to do it all properly (being lazy is easy).
Coaching will definitely help, my local tri club does weekly pool sessions that are far from 1:1 but will get you there eventually if you keep at it. Most of it is knowing what you should be doing and recognising when you're not doing it.
You'd probably get a lot from a single private lesson at your local pool. I did this a couple of years back, they gave me 5 or so things to concentrate on (rather than telling me everything that I was doing wrong) and it helped no end. Most instructors will be able to give very good advice (one of the instructors at my local pool is an ex-national swimmer, she is scarily fast and it looks effortless).
Speaking of fast and looking effortless, the cheapest option is just watch this video every time before you go swimming: https://www.youtube.com/watch?v=s3HhNlysFDs
Look at the glide and pushing the hands forward for the catch, it's not over-reaching and the body (especially the head) is staying nice and straight. Push/stretch too much and you twist your body and waste energy.
The angle of the hands through the pull is important. You want to be pushing the water behind you, not down to the bottom of the pool.
That is quick, more than 20 minutes quicker than anyone else on the day.
How? Technique and miles in the pool, but mostly technique.
I got my Swim CSS (rough equivalent of FTP) from 2:00/100m down to 1:30/100m a few years ago (i.e. 20min/km down to 15min/km). Once I got my technique dialled in it was a case of doing more and more swimming with hand paddles to build up the arm/shoulder strength needed to keep going for more than an hour at that pace. It quickly goes though.