I would argue that most collectables can be appreciated in some way that mirrors how you might appreciate artworks like paintings and sculptures. As such, I think it is entirely appropriate to consider collectables as part of an art collection.
What is a collectable?
A collectable is an object that is limited in number and typically relates to culture, such as fashion (e.g., handbags, sneakers), sport (e.g., team jerseys, trading cards, match balls), music (e.g., guitars), movies (e.g., posters, memorabilia), gaming (e.g., consoles and cartridges), animation/anime (e.g., comics, trading cards, figurines), and food (e.g., wine).
Note, that there are ‘collectable’ objects made by artists, such as skateboards and jewellery, and you might even want to throw prints into this category too, but investors will consider these as distinct from the collectables listed above because they are not the products of artists.

What are the most ‘art-like’ collectables?
I think it would have to be comics, fashion, and trading cards that resemble traditional art most closely. Thus, their inclusion in an art collection might feel right to some collectors.
I don’t think much of a case needs to be made for comic books relationship to art. Roy Liechtenstein famously adopted he style of comic books for his work, while Alex Katz, one of the most popular contemporary artists, definitely has a stylistic affinity, whether on purpose or not.
The design of sports cards can be downright beautiful and alluring, producing an effect similar to some artwork. Throw in a graphic foil for a touch of flamboyance, and you have a very nice piece of ‘art’ that would look great on the wall. I would also say the same about some cartoon/ gaming trading cards, although I hold a preference for the artfulness of sporting cards.
Regarding fashion, I find it hard to separate what a fashion designer does and what a traditional artist does. This is especially true when it comes to the very high-end fashion houses that employ ‘artisans’ to construct fashion items. The skill and dedication that these workers employ can be of exceptionally high quality that exceeds the care the traditional artist even takes. It is for this reason that fashion collectables can fit very easily into an art collection. It might even pay to mention that Hermès Birkin Bag were recently outed as one of the best investments over the past 35 years.
The downside of collectables
A possible downside you encounter if you include collectables in your art collection is that you are opening yourself up to an asset class that may operate a little differently than painting/sculpture/etc. For one, auction houses that handle collectables may not be as plentiful as those that take art collections. Further, the variables that determine the pricing of collectables will likely be different to those that govern art pricing, so you will have to learn about the intricacies of the collectables market in addition to the art market.