What previous Shimano road shifters are 10sp and exit cables under bar tape?
Shimano calls this 'hidden brake and shift cables.'
https://bike.shimano.com/en-EU/product/component/claris-r2000/ST-R2000-L.html
First on Dura-Ace 7900
There is a list of 10-speed groupsets here:
https://en.wikipedia.org/wiki/Shimano#Road_groupsets
Then:

Dura-Ace 7900
Ultegra 6700
105 5700
(Tiagra 4600 does NOT have the hidden cables and is based on an older design.)
Tiagra 4700
(Not listed there and irrelevant unless you have hydro disc brakes, but ST-RX400)

7900 and 6700 are almost identical internally (both contain ball bearings). 5700 is a bushing design, as is 4700.
4700 is essentially an R9100/R8000/R7000 design; i.e. the brake cable/lever follows 'SLR EV' design, rather than 'New Super SLR'. It also uses the 11-speed RD pull ratio (along with GRX 10 speed), which pulls more cable and is therefore easier to setup and generally better. So you can use any 11-speed RD with this, or RD-4700/RD-RX400 10-speed RDs. But not the older 10-speed road RDs.
7900 revised the brake pull ratio, so your bike will stop poorly if you mix 7900 with brakes BEFORE 7900/6700/5700/4600/3500/2400, but you can mix it with newer design (symmetrical pivots on the arms, rather than one on the arm and one on the top - symmetrical design is called SLR EV), R9000/R8000/R7100/6800/5800/5810 brakes
I would go for the 4700 brifters rather than any older ones.
In terms of FD, assuming you will use band-on, then 4700 has the long-arm design:

the increased leverage here means it should shift better than the 7900/6700/5700, design

(note that 7900/6700/5700 introduced a new pull ratio, which as indicated above did not propagate to 4600, which was older.)
[also note that the long arm created problems with cable routing on certain braze-on frames, so they updated it again for the current R9100/R8000/R7000 series)