Does @wire provide the latest updates to a record if changed on another tab, trigger, or other process?

The wire adaptor does not have Streaming built into it. The wire adaptor uses LDS cache and this blog in a good read on how all this works under the hood.

Essentially you will need a lightning Data Service along with wire adaptor if you want to listen for change from the different components on the same page.

If the action is asynchronous or on a different page, you will have to refresh the page to get the latest dataset or provide a button or an action so you can refresh and get the data.

If you need it to be automatic without manual interaction then this can be achieved using Change Data Capture or platform and using the empi lightning component.