I jumped in here simply because I saw the letters "TT".
I hope it works out for you either way. But, around here most folks I know that own something like this bought a super basic alloy TT-bike base bar. Often just the round ones that perk up at the brakes like yours. TT bike base bars can almost have the exact same bar shape you have there, but the brake cable routes internal and exits the bar underneath and near the stem.
They can be really cheap too. I've seen alloy "aero" base bars like this, with the "tilt" upwards at the end like you have there......for $70. Then you can run TT bike brakes with the cable run inside.
A clean option.
I own Selcof TT brakes bought through Planet X. Internal cable run.
https://www.planetx.co.uk/i/q/BLPXAE...t-brake-levers
Not fully internal, but would use internal cable brake then exit bottom of bar there in the pics:
https://www.racycles.com/equipment/c...SABEgIdwfD_BwE
A Deda Crononero low rider would fit the bill. Almost all internal, cheap, and same shape you have almost.