Is this a worn cassette/chain, or am I missing something?

[Ajax Bay]

I'm trying to decide if it's worth investing more time in the bike, as we'll not get more than 80€ for it.

Entirely understood. To quantify my 'not expensive' a 7sp freewheel and chain would cost £23 retail (Hal fords) in UK

 

[Andy in Germany]

Even if you only get €80, is it good training for the client? Able to see the before and after repairs.

A very good question. As it happened I got the best of both worlds: I asked a client to look at the bike, and as soon as they saw the chain as shown above they surprised me by identifying the problem.
"Could you change if for me then?" I asked.
"Yeah sure".
Much better; now they know I know they know the problem, and they know I trust them, and I can do something else. Result.

 

[Andy in Germany]

Entirely understood. To quantify my 'not expensive' a 7sp freewheel and chain would cost £23 retail (Hal fords) in UK

We have them in stock, so it would be possible. As described above the situation has worked out quite well, and that was worth the material costs.