Providing 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. As for the message that you are seeing, there are multiple possibilities - including an attempt by a threat-actor attempting to obtain your account credentials.
Have you tried to access your Google Account using a browser from a different computer? When you do so, don’t respond to any links that you may have received - but instead type the URL directly into your browser. Once signed-in, as a precaution, you would be well advised to change your account password along with any security questions that you may have used when attempting to previously resolve your immediate problem. This is advised in case you have stumbled across a phishing attempt that was trying to obtain your account information.
Returning to your iPad…
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 expose to risk.
The majority of threats to which you will be invariably exposed will surface via web pages or embedded links within email. These browser-based attacks can be largely and successfully mitigated by installing a good Content and Ad-blocking product. One of the very best and 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 blocked form download. A further benefit on metered services, such as cellular connections where you data may be capped or chargeable, this not only improves speed but also saves you money. 1Blocker 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 measure to improve protection 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 recommend 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
2620:0:ccc::2
2620:0:ccd::2
Cloudflare
1.1.1.1
1.0.0.1
2606:4700:4700::1111
2606:4700:4700::1001
Use of the above DNS services will help to shield you from “known bad” websites and URLs - and when used alongside 1Blocker, or other Content Blocker provides defense in depth.
There are advanced techniques to further “harden” iOS/iPadOS (such as using DoH, DoT and DNSSEC). Apple has recently introduced its new Private Relay to its iCloud+ subscribers - in part employing ODoH (a variant of DoH) as an element of this new functionality.
I hope this information and insight proves to be helpful.
