Show plan types in UI + fix tags column removal

[HamptonMakes]

Makes plan types visible end-to-end:

• Type badge on homepage plan cards
• Type badge on plan show page header
• Type filter pills on homepage (only shown when plan types exist)
• Removes stale after_initialize { self.tags ||= [] } since the tags column was dropped by the tag model migration

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[chatgpt-codex-connector]

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[chatgpt-codex-connector]

Keep tags default until tags field is fully removed

Dropping the tags initializer here changes newly created plans from tags: [] to tags: null while the rest of the app still treats tags as a live field (the schema still has coplan_plans.tags, and the API continues to read/write tags). In practice, a client that creates a plan without sending tags now gets a nullable shape instead of an array and can break if it assumes iterable tags based on the documented/update contract. Keep the default ([]) in place until the column and API exposure are removed together.

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[HamptonMakes]

Re: Codex review on tags initializer — the tags JSON column was removed by the Tag model PR (#79), which replaced it with a coplan_plan_tags join table. The column no longer exists in the schema, so keeping after_initialize { self.tags ||= [] } causes a NoMethodError. This removal is correct.