Here is the final result of the topic.
I went to the store, my selection of MBP 2021 14" was ready to be picked up.
The manager worked on the thing a bit, took almost 30-40 minutes to be completed.
I did not pay for the battery replacement, which has never been done, as 209 Euro. The manager has apologised me for the inconvenience and misunderstanding, and they waived it off.
At the end, I received the brand-new 2021 14" MBP base-model, and now I am writing on this computer. (For now it does not feel like my early 2015 lovely MBP, however it is damn fast, I liked.)
The manager also has given me 2 Apple USB C to USB A dongles, for free, gift.
I also added AppleCare+. I asked about it to the manager, he told me that it is completely up to me, but is beneficial. Especially the 3 years coverage seems so nice. And if I ever drop my computer or maybe my coffee spills on it, even the most expensive repair like maybe motherboard, would cost me 249 Euro. Normally it is more than 1000, he said. So I just accepted the AppleCare+, student discount was 10%, so I paid 269 Euro for it.
For the difference between 2020 and 2021 MBPs, I paid 480 Euro. I guess this is really acceptable. It would be better if they could give me the 2021 directly, however I can understand them as well.
Long story short, I am grateful that there are lots of respectful users, who tried to help me by sharing comments, ideas, and experiences. I am so happy to have this interaction with you all, even in negative comments.
Here is the closing part, happy pictures! ☺️