>As I understand it, each node would be aware independently of x transactions waiting for confirmation, the transaction pool.

Each long-running node would have a view that is roughly the same as the view of every other long-running node.

However, suppose a node, Sleeping Beauty, was temporarily stopped for a day (for various reasons) then is started again. That node cannot verify what the "consensus" transaction pool was during the time it was stopped -- it has no view of that. It can only trust that the longest chain is valid -- but that means it is SPV for this particular rule.

>If next blocksize is broadcast with the completed block it would be a simple matter to back confirm that.

It would not. Suppose Sleeping Beauty slept at block height 500,000. On awakening, some node provides some purported block at height 500,001. This block indicates some "next blocksize" for the block at height 500,002. How does Sleeping Beauty know that the transaction pool at block 500,001 was of the correct size to provide the given "next blocksize"? The only way, would be to look if there is some other chain with greater height that includes or does not include that block: that is, SPV confirmation.

How does Sleeping Beauty know it has caught up, and that its transaction pool is similar to that of its neighbors (who might be lying to it, for that matter), and that it should therefore stop using SPV confirmation and switch to strict fullnode rejection of blocks that indicate a "next blocksize" that is too large or too small according to your equation? OR will it simply follow the longest chain always, in which case, it trusts miners to be honest about how loaded (or unloaded) the transaction pool is?

The transaction pool is specifically those transaction that are NOT in any block, and thus, are not safe to depend on for any consensus rules.