Please allways update your release page to the new version of the software to verify so users don´t check for the wrong version.
At the moment of viewing, software is version 3.42-1, while release page version checking is for version 2.18-1.

While most users will eventually see what they do wrong, some may find it a hassle or annoying or something else.

This will most probably be a one-time visit. I did not see an email address to the author so I chose this guest post.

Linux has the problem of obtaining the PGP key securely. The user has to download it from Tixati's website which is a weaker form of authenticity (due to the whole Certificate Authorities issues). Key directory servers or whatever they're called are garbage. I'm not sure there's an elegant solution for this.

The file name in the instructions is just an example. The instructions could say it's an example and can be done for all newer versions in the same way, though.
The only other improvement I can think of is to instruct users to use the gpgv command instead of gpg.

Windows has stronger verification with Authenticode, because the certificate is chained from Microsoft as far as I know. The instructions already mention Authenticode.

Android has built-in signatures like Windows Authenticode, although contrary to Windows, the signatures are mandatory, and enforced by the OS to be matching when updating the app. It's like Windows Authenticode, but always enforced by the OS on all apps. The problem is still obtaining an initial installation that's authentic. The way to bypass the aforementioned weakness of website security is to distribute the app in an app store which can be installed securely on devices or already pre-installed on them. Google Play Store is not an option, because all new apps on Google Play Store must upload the app's signing key to Google, which means Google and anyone who hacked them could create a compromised version of Tixati for some users without the developer's awareness. There's a new app store aiming to let app developers retain control of their app signing key:
accrescent.app/
It can already be installed securely on GrapheneOS, and maybe in the future it would come pre-installed in certain brands of Android phones.
The instructions could point users to install Tixati from this or similar app stores instead of from the website or Google Play.

(To the Tixati developer: Please don't upload your Android app signing key to Google. And if you set the Google Play version to use a separate signing key to be uploaded to Google, please also use a separate package name so it could be used side by side with the “real” Tixati signed by you and not hijack its place.)