Why would you not go $6,341,151 for Cirelli and keep the 2nd round pick? Do you think $150,000 makes the difference?

Tampa would match any offersheet for Cirelli under $7.5m.

What would be the incentive for Rangers to be able to shift Smith? Is a 3rd round pick as a makeweight about right?

As it happens I recently included Smith as a cap dump to the Avs in this AGM:
https://www.capfriendly.com/armchair-gm/team/1728643

As per my trade description in the AGM, the logic of a Smith capdump to Colorado would be as follows:

Rangers perspective:
- Rangers need to move one of Staal or Smith in order to create space at LHD for their upcoming prospects (i.e. Hajek, Rykov, K'Andre Miller, Robertson).
- They also need capspace to resign Strome, DeAngelo, and Georgiev.
- With Staal having a NMC and thus impossible to move, Smith is the obvious choice. With a flat cap Rangers will find it hard to find a taker though, and thus use the lower of their 2021 3rd's to make it worthwhile to a team with unused capspace.

Colorado's perspective:
- Rather than go into the season with $5-6m in unused capspace, Avs weaponise it to pick up an extra draft pick. In Smith they also get a player who can still provide depth at both LHD and LW.
- Smith is an UFA in 2021 so this only affects 1 year. His base salary for 2020/21 is only $2.35m which despite his caphit isn't unreasonable dollar-wise for a depth guy.
- This move would still leave Colorado with over ~$1.5m unused capspace, meaning that there will be enough cap accrual by the deadline to still add a good player for the playoffs.

It would take more than a 3rd. As a comparable, Steve Mason had one year left @ $4.1M when the habs acquired Armia, a 4th and a 7th for Bourque, who had no value and was just taking up a roster spot.

The arguement that smith could be useful depth is no different than arguing Mason could have been a backup goalie.

Armia at that time carried the value of a ~ 2nd, so it took a 2nd, a 4th, and a 7th to offload that cap hit.

Nobody is going to help the rangers for a 3rd round pick.

Perhaps I underestimated how bad Brendan Smith has become. He played 62 games this season though so surely he can't be 'that' bad, or am I wrong?

Regarding Mason, I think moving a goalie as a cap dump is probably harder to do than a skater. Teams only carry 2 goalies after all, so having a terrible 'cap dump' goalie would be far more noticeable to the roster than a 7th defenseman who's a capdump.