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Fixes #15413 ### What problem does this PR solve? In **Settings → Model providers**, the *Available models* panel lets you filter providers by model type (All, LLM, Embedding, Rerank, TTS, ASR, VLM, …), but the filter tags gave no hint of how many providers fall under each type. Users had to click a tag to find out, and an empty category looked identical to a populated one. This PR adds a count to each filter tag in `AvailableModels`: - The **All** tag shows the total number of providers currently listed. - Each model-type tag shows how many providers offer that model type. - Counts respect the active search term, so the badge always matches the number of cards shown once that tag is selected. - Each provider is counted once per model type (deduplicated via a `Set`), so a provider that lists the same type more than once isn't double-counted. Counts are rendered with `tabular-nums` for stable width and dimmed via `opacity-60` so they read as secondary to the label. No API changes; the existing filter logic is untouched — this is purely an additive UI affordance. ### Type of change - [x] New Feature (non-breaking change which adds functionality)