This was alarming since I use a TP-Link router, so I tried figuring out to what extent it's able to inspect and record regular (encrypted) traffic. My TP-Link Archer AX50, running software version "1.0.11 Build 20210730 rel.54485(4A50)" is doing at least some sort of DPI on outgoing connections. I found a page in its settings (Advanced -> Security -> Antivirus -> History) that contains a log of connections I've made…
It could be doing reverse lookup on the IP you connected to? That's what a lot of network monitoring tools do.
In this case the site I tested with had a few different subdomains backed by the same IP, which I verified from a remote VPS. Using `curl` locally, with the `--resolve` flag to bypass DNS resolution, caused the router's log to contain entries for the specific subdomains requested.