feat: exclude AI Bridge usage from AI Governance seat counting (#27280)

Under the new `ai-gateway-seat-exclusion` experiment, AI Bridge usage
stops counting toward AI Governance seats.

## Seat recording

Under the experiment, `RecordInterception` no longer records
`ai_seat_state` usage for the initiator: AI Gateway access is licensed
by the AI Governance add-on rather than per seat. This experiment is
independent of `workspace-capable-licensing` (#27279) so the two
licensing behaviors can be enabled separately. Task workspace builds
still claim AI Governance seats.

## Manual verification

Verified live on a dev deployment (provider chained to dev.coder.com's
gateway, model `gpt-5.6-luna`): with the experiment off, the first
bridge request from each identity type (admin, plain member, service
account) wrote an `ai_seat_state` row (`aibridge` reason); with it on,
requests recorded interceptions but left seat state untouched — no new
rows, and existing rows' `last_used_at` did not advance.

Part of the gateway-accounts feature.

## Stack

Part 2 of the gateway-accounts stack:

1. **#27279**: permission-based license seat counting. Behind the
`workspace-capable-licensing` experiment and gated on the AI Governance
add-on, `user_limit` counts only users the RBAC engine authorizes to
create workspaces.
2. **This PR**: stops AI Bridge usage from claiming AI Governance seats
under the new `ai-gateway-seat-exclusion` experiment.
3. ~~**#27281**: adds a `use_shared` capability precondition for
workspace ACL grants, so workspace sharing is ineffective for (and
rejected toward) users without workspace capabilities, evaluated live on
every authorization.~~ This will be done in follow-up work when we have
time to look into the performance impact.

Related but independent: **#27278** hides the Workspaces page create
CTAs for users without workspace-create permission.

coderd/apidoc/docs.go

@@ -20126,12 +20126,14 @@ const docTemplate = `{
                 "nats_pubsub",
                 "minimum-implicit-member",
                 "workspace-capable-licensing",
+                "ai-gateway-seat-exclusion",
                 "ai-gateway-cost-control",
                 "chat-advisor",
                 "chat-virtual-desktop"
             ],
             "x-enum-comments": {
                 "ExperimentAIGatewayCostControl": "Enables AI Gateway cost control functionality.",
+                "ExperimentAIGatewaySeatExclusion": "Excludes AI Gateway (AI Bridge) usage from AI Governance seat consumption.",
                 "ExperimentAutoFillParameters": "This should not be taken out of experiments until we have redesigned the feature.",
                 "ExperimentChatAdvisor": "Enables the advisor tool for root agent chats.",
                 "ExperimentChatVirtualDesktop": "Enables virtual desktop and computer use provider for agents.",
@@ -20156,6 +20158,7 @@ const docTemplate = `{
                 "Enables embedded NATS pubsub.",
                 "Allows organizations to deviate from the default organization-member roles, in support of Gateway Accounts.",
                 "Counts only users holding the workspace-create permission toward the license seat limit.",
+                "Excludes AI Gateway (AI Bridge) usage from AI Governance seat consumption.",
                 "Enables AI Gateway cost control functionality.",
                 "Enables the advisor tool for root agent chats.",
                 "Enables virtual desktop and computer use provider for agents."
@@ -20171,6 +20174,7 @@ const docTemplate = `{
                 "ExperimentNATSPubsub",
                 "ExperimentMinimumImplicitMember",
                 "ExperimentWorkspaceCapableLicensing",
+                "ExperimentAIGatewaySeatExclusion",
                 "ExperimentAIGatewayCostControl",
                 "ExperimentChatAdvisor",
                 "ExperimentChatVirtualDesktop"