A lot here revolves around how much value you place on keeping the bike setup with SRAM 10. A subquestion is how much value you place on keeping it 10-speed at all.

Keeping SRAM 10 road bikes going is getting increasingly difficult. Most of the legacy support components for them that are still made are Red-level, and there are often availability gaps there too. If the Doubletaps and the derailleurs have 10 years of use on them and are wearing out as they do, there's basically no way it's worth it.

If on the other hand everything else was good and the only thing you needed were new calipers for whatever reason to keep the bike going, that's not really a problem. Just get the Apex HRD post mount calipers, which will work with everything else here. Note though that there's probably a replacement seal and piston kit available for your HRD700 set if that were the issue.

In Shimano land, yes the hydraulic road STIs work with post mount mountain brakes like they were meant to do so. The first Shimano road hydros basically were just M785 calipers with different cosmetics. But if you were to go this direction, you're talking about buying STIs, both brakes, and the RD no matter what. SRAM and Shimano front derailleurs and shifters interchange somewhat, so you could perhaps get away there. Your 10-speed cranks will also typically be able to work with 11 if you went that direction, since you're also somewhat boxed in if you were to only be looking at 10-speed Shimano road groups.

If the SRAM rotors you have are still good, it won't really hurt anything to put the new calipers on them.

A lot here revolves around how much value you place on keeping the bike set up with SRAM 10.

Keeping SRAM 10 road bikes going is increasingly difficult. Most of the legacy support components for them that are still made are Red-level, and there are often availability gaps. If your Doubletaps and derailleurs have 10 years of use on them and are wearing out as they do, there's basically no way it's worth it.

If on the other hand everything else was good and the only thing you needed were new calipers for whatever reason to keep the bike going, that's not really a problem. Just get the Apex HRD post mount calipers. Note though that there's probably a replacement seal and piston kit available for your HRD700 set if that were the issue.

In Shimano land, yes the hydraulic road STIs work with post mount mountain brakes like they were meant to do so. The first Shimano road hydros basically were just M785 calipers with different cosmetics. But if you were to go this direction, you're talking about buying STIs, both brakes, and the RD no matter what. SRAM and Shimano front derailleurs and shifters interchange somewhat, so you could perhaps get away there. Your 10-speed cranks will also typically be able to work with 11 if you went that direction, since you're also somewhat boxed in if you were to only be looking at 10-speed Shimano road groups.

If the SRAM rotors you have are still good, it won't really hurt anything to put the new calipers on them.