I've taught a lot of adult beginners. My guess is you're comfortable in the water and already fit. So if you have access to a pool and a half decent teacher you'll be more than fine.
About 9 years ago I taught a lady in her 60s to swim well enough to swim the straits of the bosphorus. That's about 2km of open water swimming. She had less experience than you.

I'm so glad I saw this thread!! In 2012 I began my journey into endurance sports wanting to do triathlon but I couldn't swim! I did a couple tris and thought I was going to drown, I actually came out of the water dead last on both of them. So I just kinda gave up and started ultra running. Well here I am now 9 years later at 45 years old and it's still eating at me that I gave up!! So I'm on a new mission to learn to swim. I just joined the YMCA to get started. My problem now is the same as 9 years ago, I can find zero coaches around that are willing to give private lessons to an adult and there are no masters programs here. I tried for nearly two years before looking for someone to help with no luck. So it's me and a TI book this time, we will see how it goes.

Good for you. Totally doable. TI may of changed since I used the book so take what I say with a pinch of salt. At the time I thought it was a great way to reset and think about the basics. I thought it gave me a pretty good foundation. In fact I'd recommend it if you're going to teach yourself. But the trap seems to be that you then progress by trying to swim too carefully. What Swim Smooth would call an over glider.

As you progress and then reach a plateau I'd find resources that help you understand what you need to work on at that particular time. I think we always try and improve technique but not entirely and not at the expense of fitness, strength, rhythm and timing, etc.

Something that helped me a bit was getting video of myself swimming. I have a cheap Go-Pro knock off and a suction cup thing at the end of the pool and honestly just that 10 yards of footage of me coming straight at the camera exposed a lot of flaws to work out. It's probably not as good as a coach, I've never had one so I don't really know, but you could post the videos online and get feedback on position and stroke and have a list of immediate things to work on.

Your local Y swim instructors refuse to give you lessons b/c you are an adult??? Are you abso sure about that??? I've swum at around 40 diff Ys and fitness centers and most of them offered private swim lessons for all ages. Only exception might be Gold's Gym, but ALL the Ys offered lessons to anyone willing to pay a nominal fee.

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"Anyone can be who they want to be IF they have the HUNGER and the DRIVE."

They didn't actually say they refused to and they do say they offer private lessons. But when I talk to the directors they always say something like "let me see if I can find someone that would be willing to do private lessons". They usually never get back with me and when I try to follow up they just kept giving me the same run around. They offer a lot of kids and teen classes and swim teams but I think the adult or private lessons is more the Y trying to hook a private instructor up with you, not necessarily a Y employee.

"I can find zero coaches around that are willing to give private lessons to an adult and there are no masters programs here."

Are there older swimmers from those teams (and I mean, like, HS juniors or seniors)?

I bet they'd coach you. Maybe I'm being overly optimistic, but if there's a swim team, there are probably a couple of national honor society, type-A kids out there who would be willing to work for a fair price.

Good idea, I'll keep an eye open and ask around.

I'll be 60 this year.

I'm always one of the slower ones in my age group.

If I finish in the third quartile, I'm ecstatic.

Something I figured out at my first race is that everyone likes a slower competitor.

... and something else I learned after my first sprint triathlon is that non-triathletes are impressed that I'm a triathlete. My wife makes sure it is one of the first things that new acquaintances learn about me. My standard reaction to their comments is, "Aw, shucks! It isn't like I win."