Two important informations are buried like „now smaller teams take podium 5% of time instead of of 10%” and „cost cap administration is a burden” and they there are no clear guidelines on what is in the cap and what not.
Not really. The budget cap does not include the salaries of active drivers and the three highest paid non-driver employees, as well as some other odds and ends.
In most major league sports in the US, there is some form of salary cap, but it really only applies to players. Organizations can spend money on other things as they wish. That applies to coaching, front office, facilities, etc.
In motorsport and in Formula 1 not so much. If a team has a dominant car, let's say half a second faster than the second best, the championship is an internal matter between its drivers. Any second tier driver sitting in one of those two cars can be world champion. The only opponent is the team mate. So most of the money goes into the car.
The Formula 1 cost cap applies to all expenses with few exceptions. Most notably drivers and the (3?) highest paid employees. Of course you must keep the bosses happy, right? Drivers could become subject to the cap in one of the next years. They won't be happy but what can they do? Furthermore teams will always find somebody to drive their cars even at one tenth of what they are paying now.