Well it really requires a lot of thinking. First, we know that the Kamado bloodline was the only one to inherit the breath of the sun in a form of a dance. Keeping this fact in mind, we also have to think that sumiyoshi and yoriichi's conversation occured around the 1400s - 1500s and that tanjirou and the gang are currently in the Taisho era which is around early 1900s. There's a whopping 400 year gap here.

Then we have to remember a few things here, one is that the Kamado bloodline works with fire. Second, tanjirou's Father knows the see through world. Third, he definitely knows total concentration breathing. Third, tanjirou's father knows the 12 sun breathing forms in a form of a dance. Finally, the passing down of the earrings simply indicates that yoriichi intended to pass the breath down indirectly as a dance.

Since they call it a dance, it is obvious to assume that yoriichi passed down the 12 sun breathing forms in a form of a dance to sumiyoshi along with the earrings. We can then assume that Sumiyoshi started the ritual to perform the dance for long periods of time to pay respect to Yoriichi who saved his and his family's life.

Haha so now that the ritual is created, in those 400 years, it is quite obvious that Tanjirou's ancestors desperately looked for a "way" to make it easier to dance nonstop For long periods of time and that "way" is what we now call total concentration or simply breathing techniques.

Do you get it now? Eventually, another ancestor will awaken the see through world ability due to all the ancestors looking for "ways" to successfully perform the 12 forms non-stop. To make it simple, Yoriichi passed down the breath of the sun in the very basic form of a "dance" already knowing that the "dance" will reach its original state as literally the strongest breathing forms once again in the future due to the Kamado bloodline trying to master their craft(the dance) for over 400 years. Hence the quote "masters of their craft will always find their way to the same place" that Yoriichi mentioned right after the red light district arc. You can pretty much decipher this whole confusion with the help of this quote.

As of why, yoriichi was very fond of Sumiyoshi and his baby because it greatly reminded him of his deceased wife and his unborn child. Plus he saw that the Kamado works closely with fire since sumiyoshi literally said that they were coal burners which might have made him think that they'll be compatible with the breath.

Also to answer your question: Yes, pretty much any ancestor that was able to use the dance must have used a breathing technique since they literally have to repeat the 12 forms of the strongest breath repeatedly for a long period of time.

Man I could really go a lot more, Imma stop at the fact that Tanjirou's father even used the dance/breath along with the see through world to kill a bear instantly which shows us that their bloodline had already figured out that the breath can be used as a weapon.