Legal licence

No. To use logos commercially, you need to address yourself to the rights holders (the clubs and marketing companies), who may or probably, may not be interested in doing business with you.

Editorial use only is a special licence, where you can use an asset without the right holders' authorization, like with press articles or similar. In no case, you can use those images to promote your business or to sell items, like T-shirts with the logos printed on.

As you have correctly concluded, you cannot use Illustrative Editorial images for commercial projects. However, if you find images of logos that are available for commercial use, they are theoretically not infringing anyone's intellectual property rights and you are okay to use them in your project. You should note, however, that when you download an asset and use it in your design, you do not own exclusive rights to that asset. Another Buyer can also download it and decide to use it as their logo also. You cannot trademark your logo design if it was based on an Adobe Stock license, because the original creator owns the IP for that asset.