I don't have an indoor pool but I do have an outdoor one (it was there when we bought the house). We have an air source heat pump (and electric cover) and I'd say it costs around £150-200 a month in extra electricity when in use. We were told it was meant to be a saving of £400 relative to a boiler but not entirely sure that's true (though our pool is quite large and deep). I'm sure this would be lower indoors as you don't get the same heat loss.
The chemicals are not that expensive if you do them yourself. I'd say about £100 each to close and open the pool (which you wouldn't be doing for an indoor pool). You can keep the cost of chemicals down according to the type you buy - ready made or granules you mix yourself. I'd be surprised if it cost you more than £20 a month, depending partly on the natural ph of your water (and whether that needs treating before you can add the chlorine).
But we both find owning a pool very frustrating. Again, probably far worse for outdoor pools as the machinery gets colder in the pool shed and is turned off through the colder months, but the equipment breaks regularly. We bought a new air source heat pump 10 years ago, that needed various expensive maintenance procedures such as re-adding the gas inside, and needed replacing entirely last year. Ditto for the electric safety cover, bought new 10 years ago, the ropes snap at least once each season and we've needed a new cover this year.
For the outdoor pool owners, most people don't discover the faults until they turn them on in May or June at which point it can be hard to get an engineer out for several weeks (and some won't come out at all). Engineers are expensive and can be hard to find as the equipment can be quite specialist (my pool cover specialist drives from Somerset up to London to do mine).
My kids swim but, as they get older, they don't stay in for hours as the lure of YouTube and Tiktok is too tempting. I suppose it also depends on much you love swimming - my brother in Wakefield swims more frequently in my pool over the course of the summer than I do (as ashamed as I am to admit it).