Is light a reactant in photochemical reactions?
It is neither reactant nor catalyst, and equilibrium concepts do not apply
There are processes other than photochemistry that to go in a direction away from equilibrium. They require mechanical or electrical work, and there is no established way to incorporate these into a chemical equation.
If we write a conceptual equation for charging a battery, it could look like this:
$$\text{empty battery} \ce{-&gt;} \text{charged battery}$$
The external power source is neither a reactant nor a catalyst; it is work done on the system, which serves to move the system away from chemical equilibrium.
If we write a conceptual equation for a refrigerator (or more generally, a heat pump), it could look like this:
$$\text{warm body + warm body} \ce{-&gt;} \text{cold body + hot body}$$
Again, the mechanical work done by the compressor is neither a reactant nor a catalyst, and it serves to move the system away from thermal equilibrium.
For both processes, you could not say that in the presence of work, an equilibrium is reached. It is just the opposite - we are moving away from the equilibrium.

[OP] So is photon absorption just a physical process and therefore the chemical equilibrium concept doesn't apply?

Photochemical reactions can move a reaction away from equilibrium (as in the example of cis/trans isomerization the OP mentions). This makes it a non-equilibrium process, so equilibrium concepts need to be expanded. If you want to describe the situation under certain irradiation conditions, you might use the term photostationary cis:trans ratio (see section on stilbene in https://www2.chemistry.msu.edu/faculty/reusch/virttxtjml/photchem.htm).

[OP] I read somewhere about photoisomerization and that favors the less thermodynamic stable product and that make me think of how is it possible for the value of equilbrium constant to change (considering interoconversion as a &quot;reaction&quot;).

The equilibrium constant does not change. The reaction just does not go to equilibrium (or in fact moves away from equilibrium).

[OP] First the notation hν can't be thought to be a catalyst as it doesn't make sense because isn't regenerated.

Things written on top of the reaction arrow are not necessarily catalysts. In general, that spot is used for reaction conditions, such as solvent, high temperature, or &quot;reflux&quot;.

[OP] Then how one should think about light in a chemical reaction? It is a reactant?

Some textbooks write &quot;heat&quot; as reactant or product, which already does not make sense (but is used in combination with Le Chatelier principle to memorize how equilibrium constant change with temperature). For photochemical reactions, however, there is a stoichiometric aspect to the role of photons; for every reaction, one photon has to be captured.
A comprehensive published treatment
The abstract of this paper (Perspective – life and death of a photon: an intuitive non-equilibrium thermodynamic distinction between photochemistry and thermochemistry) addresses some of the misconceptions for photochemical reactions. It is a bit long, so I am breaking it up into smaller parts.
First, it states that photons are not chemical reactants in photochemical reactions:

Neither the thermodynamically determined probability isotherm nor its kinetically manifest rate isotherm can be applied to photo-absorptive reactions such that the participants, including photons, may be treated as if they were chemical reactants. Photons and chemical reactants differ from each other fundamentally: firstly, a photon's energy is absolute and, in all instances of practical relevance to the present paper, independent of its surrounding electrochemical field, while the energy of a chemical reactant is relative and defined by its surrounding field; secondly, while both photons and chemical reactants can and do engage in entropy creation, only chemical reactants can engage in entropy exchange.

It then goes on to address the mistake of treating photochemical processes using equilibrium concepts:

Clarification of these differences requires identification and abandonment of fundamental historical errors in photochemical thought deriving from inappropriate overreach of analogies drawn between light and ideal gases, and including: treatment of photo-absorption as a reversible chemical reaction; attribution to light of thermal potential, or temperature (as distinct from the idealised abstraction of a ‘temperature signature’); attribution to light of exchangeable entropy content.

Then, it addresses how entropy plays a role in these processes:

We begin by addressing widespread misapprehensions concerning the perennially misunderstood concept of entropy and the frequently overlooked distinction between entropy creation and entropy exchange. Armed with these clarifications, we arrive at a useful perspective for understanding energy absorption and transfer in photosynthetic processes which, through the chemical ‘kidnapping’ of metastable excited states within structured metabolic pathways, achieves outcomes which the Second Law denies to thermal chemical reactions