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At the end of the last episode of season 2, the seventh signal shows up.
As I understand it, this signal is created by
Michael on her return to "the present".
Therefore, I would expect the crew of the Enterprise to be way more excited and head straight for her.
The only thing is the distance, apparently the signal is 51,000 lightyears away. That seems like a lot but I have no idea whether that distance can be traveled in any reasonable amount of time with a warp drive.
Discovery more or less answered the "Why didn't they go there?" part in the episode New Eden
BURNHAM: And it's in the Beta Quadrant, 51,450 light-years away.
PIKE: At top speed, that would take us 150 years to get that far.
Discovery's warp drive was no better than Enterprise's, so that answers the question of why didn't they go.
You missed the purpose of the seventh signal, however. From Such Sweet Sorrow Part 2 (major spoilers)
SPOCK: I only wish I could be certain of your safety.
BURNHAM: You will. I'll send the last signal. I'll send it through the wormhole when we get to the other side.
SPOCK:I will watch the stars for it.
Remember that
Burnham and Discovery went permanently into the future. So Burnham's signal is merely to let Enterprise know they made it to the future, not where she is at present
The maximum warp speed for USS Enterprise (in TOS) is stated to be warp 8. Using the old warp scale (from TOS era) this gives a speed 512 times the speed of light. Given that in one year they will travel 512 light years. This gives an estimate of 100 years of journey (one-way).
