Stabilize singular_loci's refined Tate fiber type computation (Monte Carlo) with fixed seed

[HereAround]

Aims to close #4593. (Might need rebasing should #5154 be merged first.)

[codecov]

Codecov Report

❌ Patch coverage is 81.81818% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 84.83%. Comparing base (8b3dc60) to head (d16c429).
⚠️ Report is 63 commits behind head on master.

Files with missing lines	Patch %	Lines
...xperimental/FTheoryTools/src/TateModels/methods.jl	0.00%	2 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #5156   +/-   ##
=======================================
  Coverage   84.83%   84.83%           
=======================================
  Files         709      709           
  Lines       95508    95506    -2     
=======================================
- Hits        81022    81021    -1     
+ Misses      14486    14485    -1     

Files with missing lines	Coverage Δ
.../FTheoryTools/src/HypersurfaceModels/attributes.jl	80.00% <100.00%> (ø)
.../FTheoryTools/src/LiteratureModels/constructors.jl	92.46% <ø> (ø)
...rimental/FTheoryTools/src/TateModels/attributes.jl	86.58% <100.00%> (ø)
...l/FTheoryTools/src/WeierstrassModels/attributes.jl	84.09% <100.00%> (ø)
experimental/FTheoryTools/src/auxiliary.jl	80.76% <100.00%> (+0.23%)	⬆️
...erimental/FTheoryTools/test/hypersurface_models.jl	100.00% <ø> (ø)
experimental/FTheoryTools/test/tate_models.jl	0.00% <ø> (ø)
...perimental/FTheoryTools/test/weierstrass_models.jl	100.00% <ø> (ø)
...xperimental/FTheoryTools/src/TateModels/methods.jl	66.29% <0.00%> (ø)

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[HereAround]

@benlorenz When you find the time, please take a look at this. Thank you!

[HereAround]

Thank you @benlorenz , have just applied your suggestions. Is this PR now ready to be merged? Please take another look.

[lgoettgens]

Reminder: This has a "release notes: to be added" label, but the initial comment does not have a copy-pasteable block of release notes. Please either choose a different label or add the release notes here.