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They'll be fine but probably double the price they should be if you shop around.
I've got an X280 with pretty much the same spec as that T490 (12" screen vs 14") and it is fine when I use it for everyday stuff, think I paid about £160 for that.
I've also used newandusedlaptops4u on ebay with no problems.
Personally I'd also get a Firestick or Google TV stick to connect to the projector rather than a laptop but that's just because I'm a bit lazy.
£200 for an 8th gen T480 with 16GB Ram here for instance
https://www.ebay.co.uk/itm/325547972345
My partner is looking at Lenovo on tier1 refurbs, budget upto 400 ideally grade A gives us these 2.
Will be used for connecting to projector to play disney+/netflix (and the grand tours) and then just personal admin stuff.
Is one of these likely better suited, and are they upto/overkill for the job described?