Hi mpram,
Welcome to the Apple (user-to-user) Community
This discussion thread (link below) tells how Assistive touch works with downloads ... however seems Apple Pay is needed as part of the process:
How to use Confirm with Assistive Touch w… - Apple Community
Eg: Heyyow says:
"First, have the Assistive Touch enabled.
Then, click the download button in the App Store.
Next, click the Assistive Touch,
select "Device,"
click "More,"
and there, you would see the "Apple Pay" button.
Click that,
then click "Confirm Apple Pay" with the Face ID icon above it".
VemyPaw says:
"currently (Jan 2021) there is NO way to use confirm with Assistive Touch without Apple Pay"
All the best :-)