Check examples and update as needed

[Affie]

• ApproximateConvolution Update Examples #905
• BayesTreeIllustration Update Examples #905
• TexTreeIllustration
• RobotFourDoor
• TreeAnalysis Update Examples #905
• IllustrateAutoInit Update Examples #905
• MultiHypo2Door WIP update MultiHypo2Door #906
  • Propably needs Consolidate belief messages and message channels  #459 - treeProductUp "UndefVarError: getUpMsgs not defined" (see Missing deprecation for fetchMsgUpThis #1053)
  • doCliqInferenceUp!
• MultiHypo3Door update MultiHypo3Door #907
• FixedPointIllustrationsSquare
• SquareRootTypes
• squarefixedpoint

[dehann]

Great, thanks for doing this! FYI, we should add Square Root as intro example on CaesarDocs too.

[Affie]

We need a better solution to keep the examples up to date.
Ideas:

1. We can test it as a separate CI action to at least know when it's broken.
2. We can use Documenter.jl and test it as examples.
3. Maybe we should reduce it to a few (more manageable) key concepts.

I would say 1 and possibly 3.

[dehann]

I would say definitely all three, maybe better to work along priorities. Let me try do something about 3 here quick. I have never done 2, but know it can be done. And 1. is good option too, and go there if easier.