I finally found the answer from Swashbuckle's official documentation.

Turns out I was very close:

services.AddSwaggerGen(options =>
{
    // ...
    options.AddSecurityDefinition("bearer", new OpenApiSecurityScheme
    {
        Type = SecuritySchemeType.Http,
        Scheme = "bearer",
        BearerFormat = "JWT",
        Description = "JWT Authorization header using the Bearer scheme."
    });

    options.AddSecurityRequirement(document => new OpenApiSecurityRequirement
    {
        [new OpenApiSecuritySchemeReference("bearer", document)] = []
    });
});