chore: migrate type tests to TSTyche

[mrazauskas]

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What kind of change does this PR introduce?

• [ ] Bugfix
• [ ] Feature
• [ ] Code style update (formatting, local variables)
• [ ] Refactoring (no functional changes, no api changes)
• [ ] Adding Tests
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This PR migrates type tests to TSTyche as suggested in https://github.com/okta/okta-auth-js/issues/1497#issuecomment-1975889187

@jaredperreault-okta This is a fully working example which demonstrates differences between tsd and tstyche. Perhaps it is worth considering to use a single type test runner in all @okta packages?

Does this PR introduce a breaking change?

• [ ] Yes
• [x] No

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