In the past it's done this and sent it after a while but I don't understand why it's not instant (because it's literally just sending a short URL string)?
What's the tech stack of Airdrop and what should I be checking? Is there something that is faster and more reliable I could try out?
I do this all the time to & from iOS, Mac, Android & Windows in Brave using "Send to your devices".
Simply Share > Send to your devices > [pick one]
The URL appears almost instantly on the target device / the next time that device is powered on
Snapdrop as well
What I started doing for sharing text between Mac/iOS is a Note that serves me as a pastebin. It’s promptly and reliably synced via iCloud and it just works.
Alternatively you can simply use the same Firefox profile on both computer and device and have all tabs sync'd.