Will out-of-stock products be removed from my Google and Meta product feed?

You choose. On Plugins → Sales Channels, click Settings on the channel card:

• Include out-of-stock products ticked: sold-out items stay in the feed, marked as out of stock. This keeps their history in Merchant Center, and they show again once restocked.
• Unticked: sold-out items are dropped from the feed until they are back in stock.

Click Save settings. Each channel (Google Shopping and Meta) has its own setting, so you can treat them differently. To keep a single product out of the feeds, open it, go to its Product Feed tab and set Hide from the feed to Yes.