Sorry to say it, but following satnav, or even using it in Central London, is most unwise, because satnavs are never up-to-date. The restriction for the first PCN you have posted in present on Google Street View in July 2024.
When did you last update your satnav ? Using satnav is not a reason for cancellation of a PCN because they don't absolve you of your duty to obey traffic signs.
https://maps.app.goo.gl/bYXyEBVZMFGiq4f39The second PCN is for the Stephen St junction, but in the opposite direction, so at some point you must have turned round.
https://maps.app.goo.gl/pubxANdnTEKVMCrm6Did you know what these blue signs mean ?
At the moment I can see no basis for a robust appeal to London Tribunals, the only unbiased place to get a ruling. London councils get approaching £700 million a year from PCN penalties so are hardly unbiased when considering representations.