I've been playing Wordle for about a year now, as probably most reading this thread have.  I start by playing WAFFLE, then use one of the words from the Waffle solution to start my Wordle guessing.  For me, that is more of a challenge than using the same starter word or words every day.  Waffle is another once-a-day game online. I have not looked for a 24/7 version of it.
I play the once a day versions on my laptop, and play a 24/7 version of Wordle on my phone to kill time.  I have a 24/7 Sudoku app on my phone, too, that is a great time-killer.
I finish with "Bulls and Cows" from 
www.mathisfun.com.  I really enjoy that one as well.  It's a game I used to play on paper with a buddy way back in HS during those interminable study halls, and had forgotten about it until sometime last year. To see a version of it on line brought a smile, and is now a part of my daily routine.   You can play that as many times as you want in a day.
I play a few Crossword puzzles most every day, too, but sometimes skip the M-Th puzzles since they are a bit easier than the F-Sun puzzles.  The WaPo Daily MiniMeta (M-Sat) is quick and fun. 
In the USA Today puzzles, there is one called Uni-Lingo which is fun and gets progressively more difficult to solve as the week goes on.  Once you figure out some of the 'patterns', it's a bit easier over time, but then you can challenge yourself against the timer, too.   
Great ways to kick-start the brain every morning, with coffee and after perusing BWI!