Reduce the number of p-adic parent classes

[xcaruso]

Currently, Sage has a lot of different classes for padic parents (one per precision, one per extension type), which all more or less implements the same things.
I propose to simplfy this.

Depends on #23218

CC: @roed314 @saraedum

Component: padics

Issue created by migration from https://trac.sagemath.org/ticket/25973

[roed314]

Dependencies: #23218

[roed314]

comment:1

This ticket should certainly wait for #23218.

[xcaruso]

Description changed:

--- 
+++ 
@@ -1,2 +1,2 @@
-Currently, Sage has a lot of different parents for padics (one per precision, one per extension type), which all more or less implements the same things.
+Currently, Sage has a lot of different classes for padic parents (one per precision, one per extension type), which all more or less implements the same things.
 I propose to simplfy this.