Check attribute table referenced foreign key

No this isn't possible.

I'd probably create a separate table categoriesWithArticles that holds the relevant categoryids (instead of having the flag) and have the FK reference that table instead.

Another more convoluted way to enforce it and keep the column would be

CREATE TABLE categories
(
categoryId int primary key,
hasarticles bit not null,
unique(categoryId, hasarticles)
)

CREATE TABLE articles
(
categoryId int,
hasarticles as cast (1 as bit) persisted,
FOREIGN KEY (categoryId, hasarticles) REFERENCES categories(categoryId, hasarticles)
)

But this requires the creation of a technically redundant unique constraint as well as the additional persisted column in the articles table.

You need FKs in category_product table, not in categories and products:

CREATE TABLE IF NOT EXISTS categories (
    id serial,
    name text NOT NULL,
    is_active boolean NOT NULL DEFAULT true,
    CONSTRAINT PK_CATEGORIES_ID PRIMARY KEY (id)

);

CREATE TABLE IF NOT EXISTS products (
    id serial,
    name text NOT NULL,
    description text NULL,
    photo text NULL,
    price money NOT NULL,
    is_in_menu boolean NOT NULL DEFAULT true,
    is_from_kitchen boolean NOT NULL DEFAULT true,
    is_deleted boolean NOT NULL DEFAULT false,
    CONSTRAINT PK_PRODUCTS_ID PRIMARY KEY (id)    
);

CREATE TABLE IF NOT EXISTS category_product (
    cat_id integer NOT NULL,
    product_id integer NOT NULL,
    CONSTRAINT PK_CATEGORY_PRODUCT_ID PRIMARY KEY (cat_id, product_id),
    CONSTRAINT FK_CATEGORY_PRODUCT_CATEGORY FOREIGN KEY(cat_id) REFERENCES categories(id)
    ON DELETE CASCADE,
    CONSTRAINT FK_CATEGORY_PRODUCT_PRODUCT FOREIGN KEY(product_id) REFERENCES products(id)
);