matrix, docs: drop the last admin framing, fix tense and prose lint

Three leftovers from the rename, plus the gating prose job.

`nix/packages/default.nix` still described the minter as the "matrix
admin credential's minter", and shipped that claim in the package's
`meta.description` — a PR-visible string.

`promote_user_to_admin`'s doc comment pointed at the `admin_execute`
entry in `hive-matrix.nix` as the thing that bootstraps the first
admin. That entry is gone, so the comment referenced nothing. It now
records that the account is ordinary, that the call therefore has no
working sender, and that rehoming at swarm level is the fix rather than
re-granting. `reset_user_password` gained the matching warning; it had
none.

The prose fixes clear all 8 `CI / prose lint (vale, errors)` failures,
all of which were in docs this branch touches. No vale config change,
no exception, no carve-out: contractions, one recast sentence, one
de-hyphenation and one dropped "simply".

Tense: four docs described system behaviour in the future ("will
refuse", "will fetch and trust"). Reference docs get read from the
other side of the change, so they say what the system does.

docs/getting-started/setup.md

@@ -181,7 +181,7 @@ which. A hive that does **not** deploy the store names the reader's three
 itself: the operator issues that leaf out of band, and it's the one credential
 the store can't hand you, being what opens it. ⚠️ Not the gateway's HTTPS certificates and not the hive CA — this is
 **mTLS between services and the store**, a separate trust domain, because a
-store that took its identity from an authority it will itself distribute could
+store that took its identity from an authority it itself distributes could
 never come up before that authority.
 
 ### 4 · Swarm SSO (only when `deploy.authelia`)
@@ -203,8 +203,8 @@ surfaces (the swarm UI below) gate on that group, and an account
 without it authenticates successfully and is then refused — which reads
 like a broken login rather than a missing group.
 
-If an account already exists without it, `user add` will refuse rather
-than amend — adding the group afterwards is `swarmctl user update mara
+If an account already exists without it, `user add` refuses rather
+than amends — adding the group afterwards is `swarmctl user update mara
 --add-group admins`.
 
 Detail, including what the password is and why this stays manual:

docs/integrations/matrix.md

@@ -147,20 +147,20 @@ a token.
    (`hive-matrix-daemon.path` watching for `matrix-token` appearance)
    brings the daemon up on the same boot cycle anyway.
 
-### The `@hive:` account, and why it is not an admin
+### The `@hive:` account, and why it isn't an admin
 
 `@hive:<server_name>` is the appservice's own `sender_localpart`, which
 the homeserver creates itself when it loads the registration — on a
 zero-user database, inside startup, before the HTTP listener accepts
-anything. It is an **ordinary account**: nothing promotes it, and the
+anything. It's an **ordinary account**: nothing promotes it, and the
 homeserver runs no `admin_execute` for it.
 
 It needs no promotion for what the hive does with it. Creating the hive
 Space and the chat room, writing their hierarchy and join rules, and
 inviting agents into them are all ordinary client calls that ride on
 being the rooms' own creator at power level 100 — there is no homeserver
-admin in any of it. (There is no Synapse admin API here either; tuwunel
-has none.)
+admin in any of it, and no Synapse admin API to reach for either, since
+tuwunel has none.
 
 Two operations do need an admin **sender**, and neither works today:
 `hivectl matrix promote-user` and `hivectl matrix reset-password`. Both
@@ -169,8 +169,8 @@ treats a message as a command when its sender is already an admin. They
 are swarm-level operations and are being rehomed as such; until then
 they fail with the admin room's refusal rather than being served by an
 over-privileged credential that every other call site would also carry.
-The one hive-side path that depends on them is the password-reset
-auto-recovery for an agent whose stored password is gone — the ordinary
+The one hive-side path that depends on them is the automatic password
+recovery for an agent whose stored password is gone — the ordinary
 appservice re-login above is unaffected.
 
 <details><summary>Upgrading a hive that used the registration token</summary>
@@ -189,7 +189,7 @@ restarts, so the first boot after the switch already has both halves.
   and displaces no session.
 - **`@hive:` may already be an admin** on such a hive (it won the
   first-user grant when the hive was new). Nothing here demotes it; the
-  homeserver simply no longer promotes it, so a hive built fresh has an
+  homeserver no longer promotes it, so a hive built fresh has an
   ordinary account and an older one keeps whatever standing it acquired.
 - **`/var/lib/hyperhive/matrix-register-token` stays on disk**, read by
   nothing. Delete it or leave it; neither does any harm.
@@ -278,7 +278,7 @@ services.hyperhive.swarm.matrix = {
 ```
 
 **`trustedServers`** (default `[]`) — list of peer homeserver names
-whose signing keys tuwunel will fetch and trust. tuwunel enables federation
+whose signing keys tuwunel fetches and trusts. Federation is enabled
 at the protocol level from first boot (`allow_federation = true`) but
 trusts no remote homeserver until you list it here. For a closed
 single-hive deployment the default empty list is correct — add peer

docs/tools/hivectl.md

@@ -79,11 +79,11 @@ hivectl matrix invite @mara:server --room '#hive-chat:server'  # ...or to a spec
   access token path. Safe to run again — idempotent.
 - `promote-user`: promotes an already-registered user to homeserver
   admin by an `!admin` command in `#admins`. ⚠️ Needs an admin **sender**,
-  which `@hive:` is not — this operation is being rehomed at swarm level
-  and does not work from the hive today.
+  which `@hive:` isn't — this operation is being rehomed at swarm level
+  and doesn't work from the hive today.
 - `reset-password`: asks the admin room to set a new random
   password and prints it to stdout. ⚠️ Needs an admin **sender** too, so
-  it does not work from the hive today either. Useful if an agent or human lost
+  it doesn't work from the hive today either. Useful if an agent or human lost
   credentials.
 - `invite`: invites a matrix user (full `@user:server` or a bare
   localpart, qualified with the homeserver's `server_name`) to the hive
@@ -227,7 +227,7 @@ granting that group the one action `machinectl shell` needs); `choom`
 checks this itself and refuses up front with a message naming the
 requirement rather than letting systemd reject the exec later with an
 opaque polkit prompt. Same caveat as the socket grant: a shell opened
-before the operator added you to `hive-admin` won't see it until you log
+before the operator added you to `hive-admin` doesn't see it until you log
 back in — secondary group membership applies at login.
 
 It also needs the daemon socket, unlike the other exec-into-a-container