West Yorkshire . . . scenic . . . not spending much time on the middle front ring; . . . , I was thinking that a 2 speed front with 10, 11 or 12 speed rear would make more sense.
like the idea of a 50/34T front and 11-36T rear; though in reality a 48/32T front would be more appropriate
replaced the chain and rear cassette about 5 years ago. . . .
A compact (50-34t) would be fine and your current LH shifter and FD would shift between rings perfectly.
As said, you could move from 8sp to 10sp on this bike (new 10sp shifters, 10sp cassette (and chain to go with it) as well as a compact chainset (though you could go to 10sp with the triple, but why?). For 48-32t you need to look for 'sub-compact', and with an 11t smallest sprocket, you won't spin out till at 25mph+ ie a decent downhill.
Choosing a dinner plate large sprocket (eg 36t) brings challenges with capacity of the RD to cope: a reduced small ring is a better technical solution to the Riding's/rider's need for a low 'crawler' gear (length).
But you have this range already 52-42-30 and 11-30 (which is exactly what I have on my triple btw).
11sp will require new wheelset - which means N+1 is the way ahead. Your bike cannot be equipped with 12sp (the groupset and wheels will likely cost about 5 times the current bike's value).
The gear cables and outers are the originals (though I keep them well oiled).
the bike struggles between the middle and smallest front chain ring, and frequently seems to end up between two chain rings (thinking about it now: maybe that's a "sticky" gear cable?)
As for the wheelset; I do recall when I bought the bike one criticism in reviews was the Alex DA1 rims. What specifically would be improved by getting better wheels (e.g. the Vision 30, as mentioned by Chislenko)?
I understand that over the years the Shimano ranges have generally improved (such that a 2024 Tiagra should be better than my 2006 Tiagra)? Part of the reason I wanted to upgrade was that I've never been able to shift under power on this bike. I have an older mountain bike that was twice the price 5 years earlier (so a higher level groupset). That's never had any problems shifting under load, and has always been much smoother. But I don't have any experience with modern (or better) road bike groupsets.
Be kind and replace the
gear cables and outers. You may not have ridden this bike much, but the cables and outers are 17 years old! The
sticky FD downshift symptom is exactly the result of cable friction. See above the immediate 3in1 oil dribble (or
@wafter's waxing - but that requires the cable end to be trimmed and pulled out so bang another one in).
As for wheelset, disregarding the reviews, what's deficient about your wheels? Given you haven't replaced the chain for 5 years, I infer you have cycled less than 1000 miles a year (average <20 a week). The Vision30 wheels are £220. And they go round. They have rather few spokes (not good).
If keeping bike, consider replacing tyres with decent ones (see other threads for interminable discussion on choices) and brake pads: I prefer Koolstop Dura2 Salmon, ?£10 a pair, particularly on the front.
The current Tiagra groupset is 10sp (in 2006 it was Sora 8sp, Tiagra 9sp and 105 10sp). Ignoring your chainset, you have Sora (8sp) and current (modern) Sora 9sp really only differs in the '+1' and the Campagnolo style downshift thumb lever on the STIs (as mentioned upthread).
No road bike likes trying to
shift spockets under load nor to shift down to a smaller chain ring. Anticipation is key.
And that has not changed with "modern (or better) groupsets". You can get away with it in the smaller sprockets because it's a climb of only one tooth (so a 10 or 11sp helps there) but in the larger sprockets, which is where you'll be when, on a hill, you might wish to keep the power on and shift up (lower gear), the gaps will always be 2 or 3t (or even more with some 11sp outsized cassette (£50+) eg 11-36t).
So, noting the thread title, modify nothing, change the cables (that's all), and look out for a new and affordable (to you) bike with a sub-compact chainset, 11sp, probably hydraulic disc braked. There's a lot of 2020 and 2021 impulse bought bikes out there so you might find a bargain.