#1 - May 7, 2021, 8:20 p.m.
Mail is supposed to be instant between your own characters during TBC, even if it contains an item or gold. It is currently delayed still.
Mail between your own characters is not instant
#8 - May 14, 2021, 7:50 p.m.
I see that the team has been verifying a fix for this.
It will probably go to the PTR today, and should be fixed in on live Burning Crusade Classic realms when they go live on Tuesday.