I have a situation where the bike has (OEM) 8-speed Shimano Claris shifters with the cables coming out the side which interferes with the handlebar bag. (Photo below). SRAM doesn't list any 8-speed brifters at all, and Campy 8speed ergos are only available (second hand? genuine?) from Ebay. I'm looking specifically for brifters with internal cable routing - bar-end shifters are a fallback option.
There are two ways to do it.
One is use Microshift SB-R482 levers. (Sorry, I got this wrong because the image is a little tricky and it comes off a link from their front page that says "inner route cables." These have shift cable routing much like STIs with external routing.)
The other is use 10 speed Ergo levers, or 9 speed Ergo levers with the Hubbub/Shimergo mod, to shift Shimano 8 with a Shimano derailer and cassette, as outlined here. Or if you happen to find an 8-speed Ergo, you can install a 9-speed or 10-speed ratchet ring into it.
Interference with handlebar bags is a big reason why the Shimergo/Hubbub trick became a thing. You can also do the same trick to make 10-speed Ergo work with 9-speed Shimano.
SRAM started at 10 and never went backwards.
The new Claris, called R2000, has internally routed brake and shifter cables, an improvement on a previous version, that still sported the externally routed shifting cables.
It is still 8 speed group, so in line with the op's wishes.
dealers manual, page 13, how to install shifter cable: http://si.shimano.com/pdfs/dm/DM-RBSL001-03-ENG.pdf
They just recently release a new Claris internal cabling R2000 model.
The advantage of this R2000 edition of Claris is that it is 8 speed and has cable routing under the handlebar tape. Internal routing, if you will. This means that you can use it with your 8 speed bike because the cable pull will match your existing Claris derailleur while the internal cables will not interfere with your handlebar bag. Neat.
Although your pocketbook won't like this solution, the Alfine Di2 wireless brifter from Shimano does have an 8-speed option. It's not as much an internal [shifter] cable solution as a wireless shifter and internal brake cable solution.
As commenters have pointed out, the Alfine is for internal geared hubs. You might be able to bodge a solution with their Dura-Ace wireless brifters but it'll be similarly expensive and may not work.