Singularity analysis: Intelligent choice of precision

[cheuberg]

Handling of the precision parameter in singularity analysis could be improved: instead of expanding every summand with given fixed precision, the summands could get an O-term as an additional input and expand as long as their contribution is larger than the O-term (or until precision is reached for logarithmic factors with non-integer exponent).

See #17601 for the asymptotic expansions meta ticket.

Depends on #20040

CC: @dkrenn @behackl

Component: asymptotic expansions

Keywords: singularity analysis

Issue created by migration from https://trac.sagemath.org/ticket/20054