It will place the correct way for a couple fractions of a second and then changes.
https://youtu.be/KpsrM1E8IUI

on another persons pov it is the wrong way the always

oddly the flexible block placement works with hoppers

The rotations for most blocks would require a server-side mod's support. The Block rotations and offsets section on the CurseForge page explains most of this.

There is however a fallback option planned, that would fake the player rotation before placing blocks. It should allow this to work to some extent on vanilla servers, but I'm not sure how well and smoothly it will end up working, as it does need some delay between the faked rotation packet and the item use (block place) packet.

Would you suggest the Quickcarpet mod or the Fabric Carpet + Carpet-Extra mods

I would recommend QuickCarpet, as the accurate block placement support in QuickCarpet is better than in CarpetExtra.

You can get it from
Modrinth: https://modrinth.com/mod/quickcarpet/versions
or GitHub: https://github.com/QuickCarpet/QuickCarpet/releases

And if you are changing the server from vanilla to Fabric for this, then I would also recommend the Lithium and Phosphor mods, as they can greatly decrease the CPU usage of the server and thus improve performance. (If you are on 1.17 then Phosphor has not been updated just yet.)

Use Starlight instead of phosphor. It is far faster and has been updated to 1.17