Converting hybrid to gravel bike, flat to drop bars and brifters?
Unfortunately, you will find out there are no drop-bar brifters (STI, brake levers + shifters integrated) for 8 (or 9) speed that support hydraulic brakes. The lowest by Shimano are Tiagra or GRX 10-speed, but they use different cable pull ratio for shifting.
Also, the Shimano MTB brakes are not officially supported even if likely to work in practice. But yours are actually Tektro so you must inquire in their manuals whether those are compatible with Shimano road levers.
Maybe some alternative company has some hydraulic 8/9 speed levers, but be careful about the compatibility with your brakes.
One option to solve it is to use mechanical brakes instead. The other is to buy higher-end brifters and a new drivetrain (costly).
There might also be some incompatibility in the gear ranges used by your front derailleur and front road levers - not sure what here, others may know.