Title of question is self-explanatory.
Recently, it was added to the market brakes that are an hybrid mix between the mechanical Bowden steel cable and hydraulic system, which their oil tank is near the wheel disc.
I just want to know the advantages and disadvantages of this type of brakes over pure hydraulic ones.
For most of cycling history, we've actuated derailleurs and brakes by pulling cables. One of the possible disadvantages of cables in general is that as the cable housing exerts a bit of drag on the cable as you pull it through. Also, housing can get contaminated with dirt. You could ameliorate the latter problem with full-length housing, as is done on many modern mountain and gravel bikes, but more housing = more drag.
More recently, disc brakes actuated by hydraulic lines emerged. The advantages of hydraulic lines over fully cable-actuated disc brakes were discussed in this previous SE answer: it's possible to brake hard with one or two fingers, and the calipers self-adjust as the pads wear. Also, they have a lot less drag than cable actuated systems, even though you (obviously) have to run a full length hydraulic hose to the brake. Last, that sealed system doesn't get contaminated in normal operation. The best hydraulic disc brakes are better than the best cable-actuated disc brakes. To my knowledge, almost all mid to high end mountain and gravel bikes have hydraulic disc brakes.
Quick note: Hydraulic brakes need a master cylinder. This converts force (e.g. you pulling a lever) into hydraulic pressure; in full hydraulic systems, the master cylinder is located in the integrated shifter/brake lever. This is why there are two versions (rim brake and hydraulic disc brake) of most mid to high end road bike groupsets. (There are more versions if the groupset has an electronic shifting version.)
Some cable-actuated hydraulic disc brakes exist. Here, a hydraulic master cylinder on the brake itself is actuated by a cable. Examples include the Tektro Hy/Rd mentioned by Argenti in comments and the Yokozuna Mokoto. Also, Giant's Conduct system is installed on some of their mid range bikes. This system's master cylinder mounted under the stem. Any type of cable-actuated hydraulic disc brake system pairs with traditional mechanical shifters (i.e. they use steel brake cables).
I have no personal experience with any hybrid system. However, from reading reviews, there seem to be two advantages. One, they're actuated by cables. If you have mechanical disc brakes, you have mechanical shifters (i.e. on a road bike, shifters for rim brakes). You can thus upgrade the bike to have hydraulic braking without changing shifters, which saves some money. Two, they are likely to be easier to install than full hydraulic systems. You would often have to bleed the brakes after running the hydraulic lines in full hydraulic systems. Three, people who travel frequently often have to bleed their hydraulic brakes on arrival. With cable-actuated disc brakes of any sort, one can install a splitter in the cable that disconnects for packing. There may be decouplers for hydraulic systems that accomplish the same thing, but these don't seem to be well developed yet (see some of the author's statements in this review of a travel bike that used mechanical disc brakes).
Additionally, there are probably the usual pros of disc brakes over rim brakes: you have increased braking power (conditional on having a good pad compound), and the brakes may work more consistently in all weather conditions.
Do note that some semi-hydraulic brakes may self-adjust (as the pads wear) and some may not. Yokozuna's system does not, as stated in its Cyclingtips review, but Tektro's system does, as stated in the Road.cc review.
Hybrid hydraulic systems do appear to retain some of the cons of cable-actuated disc brakes: you are pulling a cable through a housing, so there will be cable drag, and even more so if that's a full-length housing (from the brake lever all the way to the brake, as you would have to do on bikes with internal cable routing). They may also need more lever pull to produce the same braking force than in a full hydraulic brake system.
So, why is Giant equipping some newer bicycles with its Conduct system versus just giving them full hydraulics? I'd speculate this is to hit a price point and/or to provide partially hydraulic braking options to bikes equipped with Shimano Tiagra and Sora groups, which are relatively low end road groups that lack hydraulic brake options to begin with. Once you get up to a bike equipped with Shimano's 105 groupset or the equivalent, I would question why not just equip the bike with regular hydraulic brakes.
As a side note, it appears that Giant is selling the Conduct braking system at retail for $200, which includes the master cylinder mounted to the stem, both calipers, hydraulic hose, and cables to go to the shifter/brake levers. It appears that the master cylinder needs to mount to a Giant stem as well, and that is not included in the kit. I can't think of a reason to recommend that anybody buy this at retail.
I believe the Tektro cable/hydraulic system has sealed the hydraulic end and, therefore, never needs bleeding. That, combined with its self adjusting feature as well as any simple manual adjustment on the cable side, makes it advantageous over purely hydraulic brakes, except that full hydraulics have more power available than does cable/hydraulic systems.
