I would like to say It is very flustering to try to make a PCB , And you find that the simplest and most used parts or not in Fritzing , Here are a few I could use a 18650 battery ,. A TP4056 Battery charging module made and placed in there too . the LM 317 And the IRF540 /570 voltage regulator .
You just have to do a little work (and/or learn to make parts which is a lot harder). A google search for “fritzing part 18650 battery” Turns up a couple of cases (I remember helping someone with one some time back). There looks to be an 18650 battery in the adafruit library (which isn’t loaded by default in to Fritzing, but there are instructions on their site on how to load it as I recall). Same with the TP4056 charging module, there is one in someone’s github repo. The LM317 can be made by changing the name of a 7805 (the cases are the same) the IRF540 and IRF570 are standard TO220 mosfets so the basic mosfet in core parts (the through hole version) will do for them. If a part you download from somewhere doesn’t do what you need post here and one of us may fix it up for you.
No EDA is ever going to have every part invented, so the FZ crew came up with generic parts that you just type the specific part# in it’s Inspector box.
I was playing with the massive KiCad5 and it didn’t have as good an Arduino library as the tiny FZ.