If I ignored the sign "beware of the bull" on the gate into a field and climbed over the gate, ignoring the warning, and were then tossed by the bull, I wouldn't bother complaining to the farmer. If I did, I would probably get the answer: "Well, I warned you to beware, and you did not beware.".
The Cambridge online Dictionary gives examples of its use, all of which match the idea that 'beware' is never used as an ordinary verb. The examples are of imperative or modal usage.
https://dictionary.cambridge.org/dictionary/english/beware
The fact that beware is not used in all the ways of other standard verbs does not entail that there is a rule against such usage. People don't tend to use it as an ordinary verb for an understandable reason.
Beware is made up of the verb be, and ware. There is a useful account of this in Etymonline: [https://www.etymonline.com/search?q=beware&ref=searchbar_searchhint]
So it was originally (in the 12th century CE) indeed not an ordinary verb to be used in different tenses. "Be" is the base form of the copula, and the base form of verbs is also the imperative form. That did not stop two famous English writers, Dryden and the good Dr. Johnson (the author of the first English dictionary). It is fair to say that some uses seem weirder than others, and that in any case, its main use is on notices rather than in conversation. The word beware for the purposes of everyday language looks moribund. That is a prediction that it will come to look increasingly old-fashioned and so become non-standard. But that does not render it incorrect or forbidden.