There are several ways to form a plural in German, including adding -e, -en, -er, -s or nothing at all; and any of those combined with adding an umlaut or not.
So some words only change in the plural by adding an umlaut (e.g. der Vater, die Väter; der Apfel, die Äpfel) and some words do not change in the plural at all, including masculine nouns in -er referring to "thing which does" or "person who does" such as Bohrer, Zeiger, Kleber; Lehrer, Bäcker, Bauer "drill, pointer, adhesive; teacher, baker, farmer".
And this sentence can be said probably across all Germany, thanks to their awesome training program for most professions and their excellent bakery tradition - man, I really miss the immense piece of high quality multi-flour and multi-seed piece of Brot I could take in LIDL for just one euro.
"Beckrei" or "Becker" Are both bakery correct?
No; neither of them is even a word.
Bäcker is a baker -- the person who makes bread.
Bäckerei is a bakery -- the workshop where the baker works (and by extention, the shop where baked goods are sold).
Where things get a bit confusing is that "at the bakery" might be translated as beim Bäcker (literally, "at the baker's").