Вот, что нашла, например:
If I am already 45 or older, can I still enter Germany as a skilled worker?
Yes. If you do not qualify for an EU Blue Card and your gross annual salary will be less than 45,540 euros, you must also present proof of adequate provision for your old age. Such proof may be provided in the form of a statutory pension insurance scheme in your country of origin or in another country, private pension or life insurance policies, or real estate and other assets.
Это как раз 3800 в месяц. Так что, все правильно.
Но может быть, пенсионная выписка из российского пенсионного фонда (например) поможет?
https://www.auswaertiges-amt.de/en/skilled-worker-immigration/2304796?openAccordionId=item-2304808-5-panel