You are correct, the new “Cards” and “Identities” sections are in fact sub-sections of the “Autofill Suggestions” section.
So the behavior on filtering for Type=Card or Type=Identity seems to be that the subsection heading (“Cards” or “Identities”, respectively) is hidden when the results are displayed.
This does not seem to be equivalent to the old “Tab” structure, in which the URI-matched login items had their own section, on equal footing with the “Cards” and “Identities” sections. Perhaps one could make a convoluted argument that the structure is equivalent, if one interprets the new UI as having an “implied” sub-section for login items at the top of the “Autofill Suggestions” section, but with a sub-section heading (“Logins”) that is always hidden (not just when filtering for login items).
So this is even worse than I had thought, because it seems unlikely that Bitwarden will be amenable to implementing collapsibility for sub-sections within the “Autofill Suggestions” section (and collapsing the entire “Autofill Suggestions” section will not help, if the cards and identities are embedded therein).
As noted above, my initial impression was incorrect — the cards and identities are not moved into the “Autofill Suggestions” section when filtered, as they are already there. What seems to happen when you filter is that the subsection headings become hidden.
This design creates unnecessary scrolling and/or clicking to use cards and identities. The option should be renamed from “Always show cards/identities as Autofill suggestions on Vault view” to just “Always show cards/identities as Autofill suggestions on Vault view”, and the “Cards” and “Identities” sections should be top-level sections (not subsections). Furthermore, all top-level sections (“Autofill Suggestions”, “Favorites”, “Cards”, “Identities”, and “All Items”) should be collapsible.
For a user who does not open the browser extension when autofilling login credentials, this would allow easy access to cards and identities (by collapsing “Autofill Suggestions”, and perhaps also the “Favorites” section).
When it comes to searching and filtering, in my opinion, the “All Items” section should actually show search/filtering results for all vault items — the “All Items” area should not exclude those items that are also shown in other sections (“Autofill Suggestions” and “Favorites”, as well as "Cards and “Identities”, if Bitwarden ends up taking my advice). The search terms and filters should be applied to all non-collapsed sections on the Vault view (“Autofill Suggestions”, “Favorites”, “Cards”, “Identities”, and “All Items”). That way, someone who needs to search within their autofill suggestions or within their favorites could expand the corresponding section(s) when searching or filtering. Others, who do not want autofill suggestions or favorites to be prioritized when searching/filtering, would be able to collapse the “Autofill Suggestions” and “Favorites” sections, but expand the “All Items” section when searching.
There could even be a customizable option that allows users to specify which sections are to be collapsed/expanded when searching or filtering.