DateTime(Immutable) will roll-over dates and there's currently no way to disable this. You can detect when this happens using ::getLastErrors(). See  https://www.php.net/manual/en/datetime.getlasterrors.php

I have a utility method that throws exceptions on errors creating a DateTimeImmutable object (the exception message contains the first error encountered, but there's not usually more than 1 in my experience):

    public static function createImmutableFromFormat(string $format, string $time, \DateTimeZone $timezone = null) : \DateTimeImmutable
    {
        $dt = \DateTimeImmutable::createFromFormat($format, $time, $timezone);

        // DateTime errors/warnings can occur even if the object was successfully created (eg. invalid date)
        $errors = \DateTimeImmutable::getLastErrors();
        if (count($errors['errors'] ?? []) > 0) {
            /** @noinspection LoopWhichDoesNotLoopInspection */
            foreach ($errors['errors'] as $pos => $msg) {
                throw new \InvalidArgumentException($msg . ' @ character ' . $pos);
            }
        }
        if (count($errors['warnings'] ?? []) > 0) {
            /** @noinspection LoopWhichDoesNotLoopInspection */
            foreach ($errors['warnings'] as $pos => $msg) {
                throw new \InvalidArgumentException($msg . ' @ character ' . $pos);
            }
        }

        if (! ($dt instanceof \DateTimeImmutable)) {
            throw new \InvalidArgumentException("Invalid DateTime value specified");
        }

        return $dt;
    }

Apparently, this roll-over behavior is not documented (besides in
an example[1]); I think we should improve that.

[1] <https://www.php.net/manual/en/datetime.construct.php>

> DateTime(Immutable) will roll-over dates and there's currently no way to disable this.    

However strtotime() function works OK   

var_dump(strtotime('2021-03-34')) outputs false

This is not a bug.
On one hand, strtotime() is supposed to parse "about any English textual datetime description into a Unix timestamp". As long as no reasonable Englishperson wants to textually describe a datetime as '2021-03-34', it makes sense that strtotime() returns false whenever its argument looks wrong according to the understanding of the common people. (There is a counterexample "35. Mai" in German literature, but that was long before the Unix epoch, and good old Erich K. actually intended it to look wrong, in order to enable crazy things to happen at this date.)
On the other hand, the creation of a DateTime object from a format is just supposed to work whenever it is possible, so it may well start from a "zero" date and the subsequently add 2021 years, 3 months, and 34 days. When I started to learn Java many years ago, the corresponding object behaved in exactly the same way.