Regarding das Gefallen, the dictionary says:
Gefallen an jemandem/etwas finden = jemanden sympathisch finden, etwas mögen
(https://de.thefreedictionary.com/Gefallen)
bei jemandem Gefallen finden = jemandem gefallen
(https://www.duden.de/rechtschreibung/Gefallen_Begeisterung_Sympathie)
Do they have the same meaning when we replace an with bei?
The two phrases are used with different subjects. You could say, there's a difference in perspective.
"Gefallen an jemandem / etwas finden" is seen from the perspective of the person who starts to like something:
Es hat einige Zeit gedauert, aber Michael hat schließlich Gefallen an den neuen Schuhen gefunden.
It took some time, but finally Michael started to like the new shoes.
On the other hand, "bei jemandem Gefallen finden" is seen from the perspective of the thing that is liked:
Die neue Ladeneinrichtung hat von Beginn an bei den Kunden Gefallen gefunden.
The new shop interior found favour with the customers immediately.
In the latter example, both the German and the English versions feel a bit clunky. Actually, the phrase "bei jemandem Gefallen finden" is a bit outdated. You may find it in older texts, or in poetic or romantic contexts.
