That's a very good expIanation, and very cIose to my personaI theory. I think it makes totaI sense that she can traveI into SiIver's timeIine just Iike sonic's, cause to me, to traveI from a worId to another, it's both traveIIing through space and time. Iike in many media when characters traveI to another worId, when they go back to their worId after the adventure, they go back to the same second they traveIIed in as if nothing happened.
And I also have a theory that there is something like Iblis in Blaze s dimension , (a parallel Iblis), which is what give Blaze her powers (parallel to Elise like you said) , and with the main dimension Iblis awakening, probably spreading wider during the 200 years time gap, it started affecting Blaze from another world, like she felt her flame wasn't right. And while in the normal time line she learned how to travel through worlds with her sol emeralds  in rush, from Eggman Nega,. In the 06 timeline, she had to do some digging herself and discover that ability just to solve the weird flame problem.
I so wanna make a fan comic about this

This is an intriguing explanation for Blaze's involvement in Sonic 06.

So Blaze, before she met Sonic, was transported to Silver's future by the Sol Emeralds on a mission to stop Iblis/Solaris to save the future and the Sol Dimension in the process. After Solaris's flame was extinguished, the timeline was restructured to before the events occurred, leading to the events of Sonic Rush, Eggman Nega's existence, a different Festival of the Sun, and Sonic Rivals.

Did Blaze leave the Sol Emeralds behind in the Sol Dimension, or did she take them with her? And if she did take them,  did the Sol Emeralds lose their power upon arrival to Silver's future, since she doesn't use them?

Nice

Can you do a video on Silver next??

Here's my revision of Sonic 06; the title would be Sonic Adventure 3. Blaze the Cat takes Princess Elise's role as Iblis's vessel. It would explore her backstory, especially how she got her pyrokinesis and why she isn't allowed to open up about her emotions. Solaris is a phoenix god corrupted by a failed project, splitting him into Iblis and Mephiles. Plus, Soleana would be in the Sol dimension. In Silver's story, he's got Future Shadow as his partner. In the final story, Burning Blaze joins the three super hedgehogs to stop Solaris. After neutralizing Solaris and restoring him to his benevolent bird form, he mends the timeline.