First things first: sending a letter on a Friday and expecting it to arrive on Monday is very risky. Yes. It can. But I don't think the carrier can guarantee that. Next time, don't do those things at the very last second. You had all February to hand in your resignation and you did it literally on the last possible day. This is Germany. There will be no repercussions, they cannot fire you, there is no point in waiting until it becomes a matter of hours and hopeful wishes and prayers that the postal worker might have a good day. Whether you are legally right or not is another question… but you could have saved all of you a lot of trouble by just sending it earlier.
For real legal advice, please ask a lawyer. This has many fine details that I might not know, or that might even have been lost by your translation into English and then by the backwards translation of this post into German.
The important thing is not when the letter ended up on their desk or when they read it. The important thing is the date when it was delivered to their legal address's mailbox. You might know those chase scenes from American movies, where finally the person catches up by tricks or plain athletics and hands the person chased down an envelope with the words "you have been served". This stupid kindergarden game does not exist here. Every legal entity (person or company) has to have an address for legal purposes. Papers count as served when they have been delivered to that address' mailbox. Whether the legal entity checks their mailbox or not is their problem. Deadlines start at date served, not the date anybody bothers to look into the mailbox.
That means if you can prove your resignation was delivered to the company mailbox on time, you are good. Typically, this is done through registered mail, called "Einschreiben" in Germany.
What I find strange is that your mail was not delivered, but brought to a collection point. That only happens to bigger packages that do not fit the mailbox (unlikely for the half page a resignation takes). It also can happen if you send it to be delivered and signed. This would be the default feature of an "Einschreiben".
This is the point where the finer details matter. I personally would think that the point of the law is that it is important it was delivered. I mean what is the alternative, I can just ignore all legal papers, if I just refuse to sign for them? Common sense says that being delivered ("served") is plenty. But common sense and "the law" sometimes clash.
If you did not send an "Einschreiben mit Rückschein" (registered mail with a paper slip as proof for you) make sure you make screenshots of all the tracking information. Normal tracking information of your carrier is not meant for long-term legal storage. It might vanish from their systems a while after the item has been sucessfully delivered. Screenshots might not be as good as the paper slip, but at least you have something.
Consult a lawyer specialized on labor law ("Fachanwalt für Arbeitsrecht"). Let them write to your employer. A lawyers letterhead does wonders to German bureaucracy. Most of the time, it doesn't even matter whether you are right. Many people will just consider the gain (another month of someone demotivated doing a token job) versus the cost (fighting with a lawyer) and consider it not worth it. It will cost you though, the lawyer will charge you. Consider this the fee you have to pay for not doing it on time, but instead rushing it last minute.
In case the lawyer tells you it actually is your fault and they are right, try to negotiate. You can have any notice period, even none at all, as long as both parties agree to it. I'm sure a company is not super keen on keeping and paying a disgruntled worker longer than neccessary. It's just that HR cannot decide that on their own. They can only look at your contract with no context or negotiation power. It is likely up to the person who signed your contract originally (or their successor) to negotiate different terms. The word for that is "Aufhebungsvertrag". Basically a contract terminating another contract on different terms than originally stated, which is only possible when both parties of the original contract agree on it.