Remove WTE from cache

This commit removes the `WallTimeEstimate` from the cache and moves it
to an isolated place. In the process, I refactored the struct to split
reporting with updating, so that reporting can be done with any
frequency/schedule desired using the same Schedule infrastructure used
by other functions/diagnostics as well.

.dev/Manifest.toml

@@ -1,6 +1,6 @@
 # This file is machine-generated - editing it directly is not advised
 
-julia_version = "1.10.6"
+julia_version = "1.10.7"
 manifest_format = "2.0"
 project_hash = "b280bcf3b481823c97fa1a62c1b5e65114b8fa18"
 
@@ -67,9 +67,9 @@ deps = ["Base64"]
 uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
 
 [[deps.OrderedCollections]]
-git-tree-sha1 = "dfdf5519f235516220579f949664f1bf44e741c5"
+git-tree-sha1 = "12f1439c4f986bb868acda6ea33ebc78e19b95ad"
 uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
-version = "1.6.3"
+version = "1.7.0"
 
 [[deps.PrecompileTools]]
 deps = ["Preferences"]