Although some have disagreed, I'd describe a Bitcoin layer as an open protocol that uses either the Bitcoin blockchain or Lightning payments network for settlement or consensus. For example, RGB uses an L1 UTXO for consensus of ownership over an asset, and it also makes use of LN to form a system of token channels.

An open protocol could be defined as software capable of being self-hosted that has an interface that other applications can make use of. This could be accessible by either RPC, REST, or embedded APIs.

One might be tempted to split layers into separate payments layers and application layers. But if one sees Nostr as Cash App, Venmo, or Strike (social payment platforms) but just in a protocol that other applications can build upon, in what traditionally would been used an API, then in every case where a layer has a financial application, it too can be a payments layer, so such a distinction doesn't make sense for the prior definition of layers.

Further, anything worth doing can have a financial application of some sort, especially if built into a protocol. Many protocols don't use money, or worse, they use their own fee token, and this inhibits their capability to scale and mitigate against bad actors.

So, I think it makes sense to call things like Nostr, Fedimint, Cashu, LNBits, Carbonado, etc., L3s. Another interesting case is the future Lightspeed Network (LSN), which builds on RGB... I would still classify it as an L3 payments network, since it helps scale Lightning with even more performance and smaller denominations of a sat. Perhaps in the bitcoinized future, LSN will be a better analog for point-of-sale Visa payments than LN, which would probably be a better analog for something like interbank FedACH.

Indexes like Electrum usually fit between L3s, so they could be considered L2s. The Ordinals index currently has no off-chain payments capability itself, so it could be classified as an L2. Non-fungible assets in most cases can only really be settled on the base layer since there's not enough liquidity for routing between multiple payment channels.