"Lo sentimos" made it longer and it was unnecessary.

"En directo" is a broadcasting term used for radio and TV to specify there are no delays in the transmission. Content being created and transmitted simultaneously is referred to as being "en vivo". In Spanish we usually either say "live stream" (without translating it, most common usage among gamers) or "transmisión en vivo" (fully translated).

"transmisión en vivo" sounds much more natural than "stream en directo". There are other instances when "stream" is more appropriately translated as stream (for example, when referring to the online streaming which allows you to watch a video without being fully downloaded), but there is no reason to use "stream" here. At the same time, "la transmisión está llena" is not a natural sentence in Spanish. You can use that expression for physical spaces, but it does sound a bit out of place for a virtual space. "Ya no queda lugar" ("there is no more room left") sounds much better.