Will all software testing eventually be fully automated, or does manual testing have a permanent role to play in developing usable products?

I think we're approaching a point where testing can be fully automated, but there will always be complex flows involving sign ups and payments where manual testing is a corner stone of the strategy. At the agency I run, we have no more manual QA testers though. Engineers write their own test and perform their own QA on features they build where needed. With a quality team that's all the manual testing I've found we need with the modern tooling we have. So we're definitely moving in the direction of less manual testing than we had ten years ago.

In my view, it will be a balance based on how much automated dev there is.

Automated code writing should be balanced with manual testing so there is at least a set of eyes across it.

Conversely, Manual coding can be supported with automated.

I don't see it as either/or. It's And

Automation testing can greatly minimize the reliance on manual testing, but it cannot entirely eradicate it. By employing automation tools and scripts, tests can be executed rapidly and with accuracy, providing benefits such as enhanced coverage and cost efficiency. Nonetheless, manual testing still holds significance in areas like user experience assessment, exploratory testing, and initial test creation. 
Human testers bring unique insights, creativity, and adaptability that automated tests may overlook. Thus, a blend of automation and manual testing is typically required to ensure thorough software testing and the delivery of top-notch products.

Any white box tests will be mostly automated. Black box tests that require UI verification and objectivity on layout, and language will likely continue to be manual, but with the new advances in AI, that may change in the future to be also automated.

We will eventually get close to a complete test automation, but the goal post will move further away at that point.  So we will always need some portion of manual testing for reasons like test to break.  The assumption of test automation is also the availability of valid test data points, which in many cases may not be possible thus needing manual intervention to do the test.