The 2.5" HDD is 9.5mm thick.
Yes, there are thicker drives (and thinner 7mm drives that work fine too though may need a spacer for some devices) but there are 2TB HDD's that are 9.5mm thick.
Actually, they even have 7mm 2TB 2.5" HDD's now.
7mm 2.5" HDD 2TB (5400RPM probably):
https://www.amazon.com/Seagate-BarraCuda-2-5-Inch-Internal-ST2000LM015/dp/B01LX13P71/ref=sr_1_3?s=electronics&ie=UTF8&qid=1529293914&sr=1-3&keywords=2tb+2.5%22
9.5mm 2.5" SSHD 2TB (5400RPM probably):
https://www.amazon.com/dp/B01M1NHCZT/ref=psdc_1254762011_t1_B00MBLX332
Not sure about 7200RPM in 2TB that is 9.5mm or less. I looked for a short while but didn't see any. Still, I'd choose 2TB 5400RPM over 1TB 7200RPM for the capacity, and performance is hard to compare because as the drive fills up the 7200RPM advantage starts to disappear (the lower RPM gets offset by the fact the same data is closer to the outer edge).
If you're sure 1TB is fine then go ahead, but the you already know 500GB isn't enough so... ?
And again, a 3.5" USB3.0 HDD is out of the question?
Also, I could be wrong but the 4TB USB drive in the following article looks closer to 2.5" dimensions so is it a 2x 2.5" (RAID0?) setup?
https://www.forbes.com/sites/mitchwallace/2017/10/27/heres-how-i-installed-a-4tb-external-hard-drive-on-my-ps4/#728f658a3e16
Anyway, that HDD is pretty unobtrusive and just needs a single cable. Here's a link to the official page right from that article:
https://www.seagate.com/ca/en/consumer/play/game-drive-ps4/
It has 1TB, 2TB and 4TB options... remember if you get a 1TB INTERNAL HDD to replace the 500GB unit you're adding roughly 465GB of usable space so you may run out of space again... heck, I have a game that uses 130GB alone.