Every connection in WP Sync declares two capabilities: whether it can be read from, and whether it can be written to. The bridge builder honours those flags, which is why an app you have connected sometimes appears in the destination list but not the source list.
Why some apps are destination only:
A connection can only be a source if the platform gives WP Sync a way to learn about new contacts, either a read API or an outbound webhook. Where a platform offers neither, the connection is honest about it and is offered as a destination only. In the built in autoresponders, four cards are destination only: AWeber Legacy, Customer.io, Mailjet and SendFox. In the Connect Pack, chat apps, help desks, databases and card printing services are destinations only, because they have nothing meaningful to read from. Stores, carts, payment processors, calendars, lead ad forms and course platforms are sources only, because their job is to report an event. So are the Events cards, the RSS Feed and PrestaShop. The posting cards, which publish a story to Slack, Discord, Telegram, Facebook, Instagram, Bluesky or Mastodon, are destinations only, and so is Meta Conversions (CAPI).
Connections that do both:
A handful can genuinely work in both directions. In the Pro Pack these are Webhook Connect, Google Sheets Connect, Zoom Connect and GoToWebinar Connect. In the Connect Pack these are Instantly, ManyChat, ProductDyno, ResultsAiX Webinars, Shape, SuiteDash and Viral Loops. Every built in autoresponder except the four listed above can also work in both directions.
The rule to remember:
The bridge builder only appears once you have at least one readable source and one writable destination connected. If the builder is not offering an app you expect, check the card on the Connections tab first, then check whether the app is source capable at all.