feat(shared): migrate the appkit CLI off the legacy workspace client

[MarioCadenas]

Part of the migration off @databricks/sdk-experimental onto the modular @databricks/sdk-* SDK (see #562). Base: feat/modular-sdk-integration.

Changes

feat(shared): migrate the appkit CLI off the legacy workspace client

doctor and the registry picker now use the facade's modular clients
(warehouses, jobs, genie, currentUser) and its raw request() seam for
services with no modular client yet (serving, volumes, vector search,
UC functions, connections, database, experiments, apps).

• Profile host is read via sdk-core profiles resolve (disableEnv), exposed
  from the facade as resolveProfile.
• Resolved host comes from getHost(), which needs no network, so it is
  also shown when credentials are rejected. The ConfigError host= parsing
  is gone.
• Existence probes classify both ApiError shapes (statusCode/errorCode and
  httpStatusCode/code), so NOT_FOUND/INVALID_VALUE/ACCESS_DENIED are kept.
• Auth hints also match the sdk-core "profile not found" and "Host is
  required" messages.
• The Lakebase probe hands createLakebasePool a legacy-shaped adapter,
  since that package calls currentUser.me() with no argument.

Draft: implemented by an agent; needs review and a deployed SP + OBO check before it's marked ready.

This pull request and its description were written by Isaac.

[github-actions]

📦 Bundle size report

Compared against bundle-size-baseline.json (main).

@databricks/appkit

npm tarball (packed): 1.2 MB (+22 KB) — gzipped download (dist + bin; excludes release-only docs/NOTICE).

dist	raw	gzip
JS (runtime)	1.3 MB (+22 KB)	456 KB (+8.5 KB)
Type declarations	461 KB (+5.2 KB)	167 KB (+1.9 KB)
Source maps	2.5 MB (+43 KB)	852 KB (+15 KB)
Other	11 KB	3.7 KB
Total	4.2 MB (+70 KB)	1.4 MB (+25 KB)

Per-entry composition (own code — deps external (as shipped))

Entry	Initial (gz)	Lazy (gz)	Total (gz)	node_modules (min)	Own code (min)
.	105 KB (+2.7 KB)	2.5 KB (+1 B)	107 KB (+2.7 KB)	external	340 KB (+8.2 KB)
./beta	101 KB (+2.1 KB)	488 B (+4 B)	101 KB (+2.1 KB)	external	303 KB (+5.6 KB)
./testing	44 KB (+1.8 KB)	32 KB (+35 B)	76 KB (+1.8 KB)	external	220 KB (+5.0 KB)
./tsdown	520 B	0 B	520 B	external	813 B
./type-generator	25 KB (+1.4 KB)	0 B	25 KB (+1.4 KB)	external	70 KB (+3.9 KB)

Chunks:

Entry	Chunk	Load	Size (gz)
.	index.js	initial	100 KB
.	utils.js	initial	4.6 KB
.	remote-tunnel-manager.js	lazy	2.5 KB
./beta	beta.js	initial	82 KB
./beta	stream-manager.js	initial	5.9 KB
./beta	modular.js	initial	4.6 KB
./beta	service-context.js	initial	4.2 KB
./beta	databricks.js	initial	3.3 KB
./beta	client.js	initial	657 B
./beta	index.js	initial	20 B
./beta	supervisor-api.js	lazy	193 B
./beta	databricks.js	lazy	180 B
./beta	index.js	lazy	115 B
./testing	manifest.js	initial	30 KB
./testing	index.js	initial	10 KB
./testing	wide-event-emitter.js	initial	2.9 KB
./testing	index.js	lazy	28 KB
./testing	remote-tunnel-manager.js	lazy	2.5 KB
./testing	utils.js	lazy	1.8 KB
./tsdown	index.js	initial	520 B
./type-generator	index.js	initial	25 KB

@databricks/appkit-ui

npm tarball (packed): 397 KB (+122 B) — gzipped download (dist + bin; excludes release-only docs/NOTICE).

dist	raw	gzip
JS (runtime)	428 KB	146 KB
Type declarations	266 KB (+341 B)	98 KB (+133 B)
Source maps	852 KB	285 KB
CSS	16 KB	3.2 KB
Total	1.5 MB (+341 B)	533 KB (+133 B)

Per-entry composition (consumer bundle — deps bundled, peerDeps external)

Entry	Initial (gz)	Lazy (gz)	Total (gz)	node_modules (min)	Own code (min)
./js	5.3 KB	49 KB	55 KB	208 KB	14 KB
./js/beta	2.1 KB	0 B	2.1 KB	0 B	5.0 KB
./react	433 KB	49 KB	481 KB	1.3 MB	177 KB
./react/beta	4.9 KB	0 B	4.9 KB	0 B	12 KB

Chunks:

Entry	Chunk	Load	Size (gz)
./js	index.js	initial	5.2 KB
./js	chunk	initial	120 B
./js	apache-arrow	lazy	49 KB
./js/beta	beta.js	initial	2.1 KB
./react	index.js	initial	431 KB
./react	tslib	initial	2.1 KB
./react	apache-arrow	lazy	49 KB
./react/beta	beta.js	initial	4.9 KB