Interesting the stuff about chimney liners (for the record OP I share your frustration and concerns).
We got our stove installed by a firm that were significantly cheaper than more established firms in the area (we still paid around £2.5k for 7.5kw Multi fuel stove plus liner and installation). One of the firms that quoted was less than complimentary about the new kid on the block but they did give us some advice at the time that was interesting.
There are a couple of types of liner you can get. One is suitable for wood burners only. A lot of installers will use this type for Multi fuel as well but it can fail due to the additional heat from coal etc.
We got a 908 liner which is rated for both.
When I asked about lining the chimney if we kept the open fire the previous owners had used we were told we didn’t need one.
Seemed odd under the circumstances but they reckoned that enough carbon etc would have built up over 80 years to mean that it wouldn’t need anything else.
Sounds like the issue is with the chimney rather than anything else.