I almost never try to found as authority, especially after the tribute changes, you're welcome to explain how you do so.
Side note: founding with authority or anything wide is much easier than with tradition.
Generally I think pantheons are in a little pathological state right now. They feel very vanilla like in design, completely different than few months ago. Of course, we needed to do something about the old wisdom or commerce because they were cancerous random faiths generators. But I hate the design of the new ones.
First of all, on deity and I think on immortal also (though I haven't played it myself), all pantheons apart from the human are gone on turn 15, and 16, for all civs, religious or not. Human is always the last to get it. This locks out most of the options. What is the point of Stonehenge if it gives you the last pantheon anyway? And it's so risky already. Tutelary gods? Expanse? Ancestor? Just forget it.
This leads to the second thing, most pantheons are just poor. They are so low in faith it's really not enough to get
The third thing is, if you are forced to make brutally suboptimal decisions in order to found a religion on deity, you just need to stop trying, because shrine into market, or walls and barracks will just not work because you need to focus on normal development, expansion, food, production, units and so on. So most of the time on deity, without several cards in your hand (natural wonder, good pantheon left, stonehenge built, isolation and safe position, faith monopoly, faith civ, lack of faith AIs) you have no chance of founding and investing into religion will cripple you so much it's not worth it.
Fourth thing, it would be much better to live with the current pantheons if the AI was doing a good job with selecting beliefs. The religions it creates are awful. Most of them aren't even useful to them. Very rare use of buildings (and no cathedrals in my games), no yields like scholarship or tithe, or diligence, even no council of elders, or apostolic tradition. AI loves spreading bonuses, asceticism, and diplomatic bonuses.
It's obvious the AI is now getting faith ABC bonuses on settling, which was not the case before. I am usually in favor of increasing them, and still see deity too easy in different aspects I wrote about in different topics, but I am not a fan of faith bonuses. You cannot plan on anything when some authority AI which has terrible pantheon, no bonuses to faith, no natural wonders, no monopoly, have four cities, and shouldn't be interested in religion can beat you by thirty or forty turns to be the last founder.
Furthermore, because pantheons are so low faith right now and the faith is locked behind improvements or population, in combination with food bonus on settling and quicker workers and techs, the AI is able to start harvesting faith much more rapidly than a human player in contrast to previous versions.