I’m contemplating spending a week or so in this area during the first 2 weeks of October, after 3.5 weeks in WA.

While researching places to stay I’m finding that several say they are closed indefinitely due to the cyclone damage, and some reopening in several months. More sleuthing seems to imply some roads have still not reopened (to Cape Trib, for example). I’m not sure I was ever aware of the damage this cyclone caused in Queensland.

October is still quite some time in the future, but I’m wondering if I should pick a different area to visit. Am I overreacting?

Are you overreacting? Yes if you imagine the entire area is flattened and out of business.

A more realistic view would depend on where you want to go & what you want to do. I'd contact the Cairns Tourist Information people & ask them about the specifics you're interested in. Much of Cairns was up & running very shortly after Cyclone Jasper but as you'd understand, some roads may take quite some time to be repaired if they were badly washed away.
https://www.cairnstouristinformation.com.au/
You could also look up the Cairns Regional Council and have a chat to them. That's what I do when I'm unsure what regional roads will be open after significant flooding.

Thanks for the tips above on who to query about the recovery from the cyclone.

Neither of them ever responded to my queries so I’m just contacting accommodation possibilities directly. So far they are more responsive.

There was an article the other day on ABC News online (Australian media company) that said the road to Cape Tribulation is still impassable and no date yet for road repair. There's almost nothing in the news here about it but it's obviously having a huge impact on the tourism operators and people who live in that area. I don't know but would guess Cairns and Port Douglas are still operating as normal. That's where most tourists go in FNQ, as well as Palm Cove, which is between the two.

I had also read that the road to Cape Tribulation was closed indefinitely. That was one of the questions I had hoped the tourism office and Cairns Regional Council would address.

Thanks for confirmation.