If this is NOT a genuine Apple branded Pencil, then that stylus IS NOT an actual Apple Pencil.
Apple Pencils come in an Apple branded box.
Other stylii ( that try and look like an Apple Pencil ) maybe cheap, third party knock-offs that claim to be compatible, but once again, may not be.
Sorry.
You seem not to want to purchase the REAL Pencil.
No one here here is going to be able to help you with getting ANY third party stylus working on your 2020 iPad Pro.
There are too many of these cheap, third party knockoffs on the market and all work slightly different.
Are you sure you even need Bluetooth connected?
Once again, many third party stylii have an on/off switch and will use a battery and NOT ever need Bluetooth to work.
The stylus you purchased maybe just another active, capacitive stylus that just simulates a normal finger touch and has NO writing pressure sensitivity OR palm rejection.
I do not know where you are from, but if you cannot afford an actual 2nd gen Apple Pencil to use with your expensive iPad Pro, then my suggestion to you is look at compatible and working stylii from Adonit.
Adonit has been with iPads for, at least, the past 6-7 years and their stylii work!
STOP playing around with cheap Apple Pencil knockoffs and get s stylus that actually works, if you cannot afford the cost of s genuine Apple Pencil.
Here is a list of all Adonit compatible stylii for all newer iPads that support the Apple Pencil.
The stylii below support natural palm rejection, pressure sensitivity and tilt sensitivity support, if applicable.
These stylii work and are somewhat cheaper than Apple's own Apple Pencil versions.
Adonit has very good customer support for all of their product offerings.
In order of low to high pricing.
https://www.adonit.net/note/
https://www.adonit.net/note2/
https://www.adonit.net/noteplus/
https://www.adonit.net/note-m/
All Adonit stylii ONLY work and are compatible with ONLY certain supported applications.
Here’s my “up to date”, comprehensive, but still incomplete, list of Adonit compatible apps for the base line iPad models, like the 6th, 7th and 8th and 9th gen iPad models, 2018-2021 iPad Pros and the 2020 iPad Air 4.
MOST apps listed support palm rejection, pressure sensitivity and tilt, unless otherwise noted
Compatible Adonit apps for drawing
Animation Desk
Amaziograph ( NO tilt support )
Art Studio Pro ( a direct Procreate competitor, just as good as Procreate )
Colored Pencil
Concepts
Forge ( drawing/sketching/concept/ideation app ) ( NO tilt support )
Infinite Painter
Interactive SketchBook ( NO tilt support )
Medibang Paint ( NO tilt support )
Procreate ( palm rejection, tilt support ONLY )
Tayasui Sketches/Sketches Pro ( palm rejection, Tilt support ONLY, NO pressure sesnsitivity )
SketchClub
Vectornator ( palm rejection ONLY )
Zen Brush 2
Compatible Adonit apps for Notes and Notes with drawing types of apps.
GoodNotes 5 ( palm rejection ONLY )
Note Shelf 2 ( NO tilt support )
Notes Plus ( palm rejection ONLY )
Notes Writer ( palm rejection improved using special, non-electrical conducting, lycra-based material drawing glove )
QuickNotes X Pro ( palm rejection ONLY. No pressure sensing for light/dark or thin/thick lines )
uPad ( app self palm rejection, NO pressure sensing or tilt support )
Zoom Notes ( NO tilt support )
PDF Pen ( NO tilt support )
This is pretty much it for Adonit compatible note-taking apps.
This stylus works with other non-compatible apps, too, but without any palm rejection and/or pressure features.
You can use this stylus with other apps but will not be able to lay your palm on the screen, while you write or draw, unless you use special, non-body electrical conducting, lycra-based material drawing glove that works by isolating your hand/palm and allow you to lay your hand/palm on the screen as you draw in these non-compatible Adonit stylus apps.
Something like these found on Amazon.
https://www.amazon.com/AKX-Rejection-Drawing-Graphic-Sketching/dp/B08R6PWKC9/ref=sr_1_33_sspa?dchild=1&keywords=tablet+drawing+gloves&qid=1611535160&sr=8-33-spons&psc=1&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUExMFg5WFBZWFpCS1kmZW5jcnlwdGVkSWQ9QTA5OTA2MzMxRUVYUURUMlAwVU4wJmVuY3J5cHRlZEFkSWQ9QTAxNDY1NjMxVjg1NE45TVRXSUQ3JndpZGdldE5hbWU9c3BfYXRmX25leHQmYWN0aW9uPWNsaWNrUmVkaXJlY3QmZG9Ob3RMb2dDbGljaz10cnVl
https://www.amazon.com/Timebetter-Rejection-Drawing-Sketching-Suitable/dp/B08DKGHYMS/ref=sr_1_21?dchild=1&keywords=drawing+gloves&qid=1611533128&sr=8-21
Many more makers of these types of gloves found on Amazon and in different hand sizes, as well!
Best of Luck to You!