In reply to J1234:
I live next to the TPT between Warrington and Altrincham and can vouch for the surface conditions not being great a lot of the time.
In particular the section between Warrington (Thelwall New Rd) and Lymm turns into a complete quagmire after even a relatively short spell of wet weather, with significant amounts of standing water (including an underpass with a foot deep permanent lake of stagnant water to get through), deeply rutted mud and parts even turning into a minor watercourse from broken drains flooding onto the trail. It's negotiable (but messy) on a mountain bike, but wouldn't fancy it on any other sort of bike. It's all down to virtually zero maintenance by Warrington Borough Council over the last few years, despite hundreds of complaints from the locals.
The rest of it from Lymm to Altrincham is a bit better, with a gravelly but in places heavily pot-holed surface. There are a lot of big puddles and a couple of minor lakes to negotiate after a wet spell. When dry, it is very dusty (with a peculiar brand of dust that is particularly erosive to chains and cassettes...).
Since the lockdown, it's all become extremely busy with local walkers, families with kids out on bikes, pushchairs, dogs etc. I've stopped using it for cycling and only go running on it during quieter times.
I'd also add that the cycling on the trail isn't really that inspiring, whilst the maze of adjacent country roads, particularly between Lymm and Altrincham, and the nearby Cheshire Cycleway, is fantastic, with quiet roads, lots of pretty hamlets and countryside views. If you are going to use touring bikes, I'd highly recommend linking a route up on those rather than using the TPT.