Fix and refactor e2e tests

[markdboyd]

Related to #66

Changes proposed in this pull request:

• Refactor e2e tests to use updated Playwright helper methods
• Update e2e tests to rely less on CSS identifiers in favor of element text that may be more durable/reliable

Things to check

• For any logging statements, is there any chance that they could be logging sensitive data?
• Are log statements using a logging library with a logging level set? Setting a logging level means that log statements "below" that level will not be written to the output. For example, if the logging level is set to INFO and debugging statements are written with log.debug or similar, then they won't be written to the otput, which can prevent unintentional leaks of sensitive data.

Security considerations

Making sure the e2e tests are passing is a critical piece of ensuring that this authentication proxy for Opensearch works as expected and guaranteeing tenant isolation of data