With available information, it is impossible to offer definitive explanation as to how this has occurred - other than to entertain the possibility that you may have inadvertently followed a link to an App Store link and downloaded the App. If the App is unwanted, delete the App from your iPad:
Remove or delete apps from iPad - Apple Support
Providing that your iPad has been kept up-to-date with system software updates, you should not be overly concerned for your iPad being directly compromised by malware. At time of writing, iPadOS 17.5.1 is current.
Due to the system architecture of iOS/iPadOS, unless jailbroken, your iPad is not susceptible to traditional malware infection per-se. However, as with all computer systems, there are still vulnerabilities and exploits to which you remain vulnerable.
For older devices, no longer benefiting from regular security updates, the risk of an unpatched vulnerability being exploited increases. Regardless of the installed version of iPadOS, there are useful mitigations that can be used to significantly reduce your exposure to risk.
Threat Mitigation
Other than malicious websites that will attempt to capture information that you willingly enter, the majority of threats to which you will be invariably exposed will surface via web pages or embedded links within email or other messaging platforms. Browser-based attacks can be largely and successfully mitigated by installing a good Content and Ad-blocking product. One of the most respected within the Apple App Store - designed for iPad, iPhone and Mac - is 1Blocker for Safari.
https://apps.apple.com/gb/app/1blocker-for-safari/id1365531024
1Blocker is highly configurable - and crucially does not rely upon an external proxy-service of dubious provenance, often utilised by so-called AntiVirus products intended for iOS/iPadOS. Instead, all processing by 1Blocker takes place on your device - and contrary to expectations, Safari will run faster and more efficiently.
Unwanted content is not simply filtered after download (a technique used by basic/inferior products), but instead undesirable embedded content is blocked from download. The 1Blocker product has also recently introduced its new “Firewall” functions - that are explicitly designed to block “trackers”. Being implemented at the network-layer, this additional protection works across all Apps. Recent updates to 1Blocker has introduced additional network extensions, extending protection to other Apps.
A further to improve protection from exploits is to use a security focussed DNS Service in preference to automatic DNS settings. This can either be set on a per-device basis in Settings, or can be set-up on your home Router - and in so doing extends the benefit of this specific protection to other devices on your local network. I suggest using one of the following DNS services - for which IPv4 and IPv6 server addresses are listed:
Quad9 (recommended)
9.9.9.9
149.112.112.112
2620:fe::fe
2620:fe::9
OpenDNS
208.67.222.222
208.67.220.220
2620:119:35::35
2620:119:53::53
Cloudflare
1.1.1.1
1.0.0.1
2606:4700:4700::1111
2606:4700:4700::1001
Security focused DNS providers intentionally "sink hole" known bad or malicious websites and resources - this providing an additional layer of protection beyond that provided by your device and its Operating System. These DNS services will, when used alongside 1Blocker or other reputable Content Blocker, provide defence in depth.
