Fix DM feature: deadlock on send, layout displacement, styling inconsistency

[Copilot]

The DM (direct messaging) feature had three critical issues: sending a message deadlocked the server, the link to DMs displaced the entire chat layout on desktop, and the DM pages used ad-hoc inline styles completely inconsistent with the rest of the app.

Deadlock fix

saveChatMessages() acquired chatMessagesMutex.RLock() while both SendChatMessage() and MarkChatMessageAsRead() already held the write lock — a classic reentrant deadlock on Go's non-reentrant sync.RWMutex. Removed the redundant lock from saveChatMessages() since callers already guarantee exclusive access.

// Before — deadlocks when called from SendChatMessage (which holds write lock)
func saveChatMessages() error {
    chatMessagesMutex.RLock()
    defer chatMessagesMutex.RUnlock()
    ...
}

// After — callers are responsible for holding the lock
func saveChatMessages() error {
    b, err := json.Marshal(chatMessages)
    ...
}

Layout displacement fix

The DMs link was injected as a standalone <div> before #topic-selector, adding a rogue flex item inside the body:has(#messages) #content flex column. Changed to append it as a tab inside the existing .topic-tabs container:

// Before — extra div breaks flex layout
messagesLink := `<div style="..."><a href="/chat?mode=messages">💬 Messages</a></div>`
tmpl = strings.Replace(tmpl, `<div id="topic-selector">`, messagesLink+`<div id="topic-selector">`, 1)

// After — DMs tab sits inline with other topic tabs
topicTabs := app.Head("chat", topicsData) + `<a href="/chat?mode=messages" class="head">DMs</a>`

DM pages restyled

Replaced all inline styles in messages.go with the app's design system classes (thread-preview card, thread-message, thread-message-header/author/time/body, card-list, unread-dot, btn, app.Page()). Pages now render consistently with mail and the rest of the app.

Renamed the feature from "Messages" to "DMs" throughout (tab, page titles, back links).

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