HP Notebook - 15-ay196nr core i7- 7th generation 7500u cpu - Is the laptop compatible with 2 tb 7200 rpm Seagate Firecuda SSHD

that is an internal drive - do you want to replace the existing o,ne? that is a 5400 rpm drive
it will be a lot faster, but SSD's are still MUCH faster, and consume less power
if you want to get it faster - choose an SSD - if the budget allows; 500 Gb drives are coming down in price
here under 180$   https://www.amazon.com/Samsung-2-5-Inch-Internal-MZ-75E500B-AM/dp/B00OBRE5UE

I will suggest you to buy SSD. it will be much faster than your existing one

If you want the highest overall performance, buy an SSD. If you want the biggest amount of storage, buy a SSHD.

and always be careful to buy a drive which will fit inside your laptop. Check the height of the exisiting drive before ordering a new one, as they do vary. Some ultra-portable laptops won't accept a 2.5in drive at all, and require an even smaller 1.8in microSATA drive.

to answer your question I must refer to HP 15 Notebook PC SPECS,  and my answer is NO.

HP 15 Notebook PC SPECS:

Supports 6.35 cm (2.5 in) hard drives in 9.5 mm (.37 in) and 7.0 mm (.28 in) thicknesses (all hard drives use the same bracket)
Serial ATA
Accelerometer/hard drive protection support
Supports the following hard drives:
750 GB, 5400 rpm, 9.5 mm
500 GB, 5400 rpm, 9.5 mm and 7.0 mm
320 GB, 5400 rpm, 9.5 mm and 7.0 mm

The file attached is HP 15 Notebook PC Maintenance and Service Guide and was my reference. page 2
c04763947.pdf

Go ahead and guy your 2TB sshd drive, SATA n UEFI  x64 took care of the limitations ages ago