Component secret management - Update core integrations

[shadeMe]

Follow the same procedure seen in https://github.com/deepset-ai/haystack/pull/6887.

~This will require a new beta release of haystack-ai. Once that's out, pin its minimum version to the integration and start porting the changes.~

Refer to this PR for an overview of the changes needed for the code - https://github.com/deepset-ai/haystack-core-integrations/pull/347

### Tasks
- [ ] https://github.com/deepset-ai/haystack-core-integrations/issues/364
- [ ] https://github.com/deepset-ai/haystack-core-integrations/issues/374
- [ ] https://github.com/deepset-ai/haystack-core-integrations/issues/375
- [ ] https://github.com/deepset-ai/haystack-core-integrations/issues/370
- [ ] https://github.com/deepset-ai/haystack-core-integrations/issues/371
- [ ] https://github.com/deepset-ai/haystack-core-integrations/issues/376
- [ ] https://github.com/deepset-ai/haystack-core-integrations/issues/377
- [ ] https://github.com/deepset-ai/haystack-core-integrations/issues/365
- [ ] https://github.com/deepset-ai/haystack-core-integrations/issues/366
- [ ] https://github.com/deepset-ai/haystack-core-integrations/issues/367
- [ ] https://github.com/deepset-ai/haystack-core-integrations/issues/372
- [ ] https://github.com/deepset-ai/haystack-core-integrations/issues/368
- [ ] https://github.com/deepset-ai/haystack-core-integrations/issues/369
- [ ] https://github.com/deepset-ai/haystack-core-integrations/issues/373
- [ ] https://github.com/deepset-ai/haystack-core-integrations/issues/330

[bilgeyucel]

JFYI, this issue requires individual updates to

• [ ] Documentation
• [ ] Tutorials
• [ ] Cookbooks
• [ ] Articles
• [ ] Integration Tiles