The Tapcart app is the mobile version of the Shopify app.
We do not provide an "out-of-the-box" integration to connect Algolia to TapCart. If you have access to the code, it should be possible to add Algolia to your application, but will require some development work.
TapCart did launch a connector with Algolia in their marketplace. This integration has been built by Tapcart, so we can not provide support for it as we don't have any experience or expertise working with it.