From a technical point of view, the only plastics that physically cannot be recycled are the plastics known as thermosets and the “cured” cross-linked relatives, paint, and tires*.
Thermosets are plastics that can not be simply melted back into a reusable form: epoxy/amine hardener (general adhesive repair); allyl/styrene-derived polyester/divinyl benzene (combo used for car dent repair sometimes); similarly derived polyester/hardener used for some tough plastic lenses and a/c windows; photocurable coatings (some types of polymer 3d printing), also the coatings on paperbacks to make them slick, and the insides of some food/beverage cans to make them water resistant, also modern dental fillings/bonding; urea/formaldehyde insulation; urethane products (foam/insulation/sealants); silicone sealants (bathroom fixtures); tile adhesives; molding compounds for art (both the mold and the molded items); Kevlar**; meringue; cellulosics cross-linked with multiple variants; Xydar**; many gels; Bakelite.
Thermoplastics have suitable properties when colder than their manufacturing process, but return to amorphous, moldable/reusable condition with heat alone.
From a chemistry pov, rubbers are just plastics with high recovery of initial size upon stretching; all the above items are plastics even if the usual appearance is not like a bottle or a cup.
*Tires are not usually recyclable as tires. They may be recycled in a sense by using them as fillers in other plastic items: benches, durable sandals… Recapping is a form of recycling, but requires the entire round structure of the old tire.
**Kevlar and Xydar are not cross-linked, but the polymer (plastic) backbone decomposes before becoming recyclable. It may be of entrepreneurial interest to use recycled Kevlar as a toughening filler.
Some things, mostly plastic, cannot be recycled practically, taking more effort to recycle than to make new. Garden hoses are an example. Styrofoam may be another, but here because of lack of commercial interest than because of adverse chemistry.
Paint is all plastic with color from a filler/pigment combination after the solvent/vehicle evaporates, and the resin, a polyester, cross-links in air. Other “paints” are the coatings on refrigerators and appliances that are cross-linked by other chemicals (baked enamels). Neither can be recovered, recycled.