Currently, you are unable to view the APKMirror web page. Instead, you get the following message shown in the screenshot below.
Tiktok downloads are currently blocked in the United States due to the Protecting Americans from Foreign Adversary Controlled Applications Act.
The link in this statement leads to the following page, containing the bill that was passed:
https://www.congress.gov/bill/118th-congress/house-bill/7521
This sets a dangerous precedent going forward for the Android community which sideloads applications onto their phones, being that APKMirror is the largest mirror of APKs for Android phones. It's also possible for them to add more apps to be included under this bill, and possible for another bill to be passed which may act as an even more broad blanket to target specific groups of people (e.g. LGBTQ+, people of color), messaging applications that are truly secure (e.g. Signal), and so on.
Then of course there a very real possibility of our president forcing the integration of software updates into both Android (and possibly even iOS smartphones) that can forcibly remove applications for the "sake of national security".
Blocked APKMirror links:
You can just login anonymously like the description you posted says. It works pretty well. It's how I download apps that aren't available on my local play store.
What does this mean?
Is it similar to Chrome's "Incognito" mode?
I'm not 100% sure but it doesn't require a login when you pick that option. Iirc it uses an account from a set of shared accounts so that it doesn't have any personally identifiable information.
And how I get ones that it says are incompatible with my device for no apparent reason.