Does Reliable Talent apply to Initiative with the Alert Feat? Does Jack of All Trades still apply in 24? /u/BadSanna DnD: Roll for Initiative!

:Alert:

You gain the following benefits. Initiative Proficiency: When you roll Initiative, you can add your Proficiency Bonus to the roll.

: Reliable Talent:

Whenever you make an ability check that uses one of your skill or tool proficiencies, you can treat a d20 roll of 9 or lower as a 10.

Alert literally says you have proficiency with Initiative. However, Initiative is not listed as a skill, nor is it a Tool, which is why I ask.

Initiative counted for Bard’s Jack of All Trades in 2014 because that ability says:

Starting at 2nd level, you can add half your proficiency bonus, rounded down, to any ability check you make that doesn’t already include your proficiency bonus.

Initiative is definitely an Ability Check.

The 24 Jack of All Trades is worded in a more complicated way that makes it somewhat questionable:

You can add half your Proficiency Bonus (round down) to any ability check you make that uses a skill proficiency you lack and that doesn’t otherwise use your Proficiency Bonus.

It still says “to any ability check,” but it also says “that uses a skill proficiency you lack,” does that mean it no longer works with Initiative, if Initiative does not count as a skill?

:Alert:

You gain the following benefits. Initiative Proficiency: When you roll Initiative, you can add your Proficiency Bonus to the roll.

: Reliable Talent:

Whenever you make an ability check that uses one of your skill or tool proficiencies, you can treat a d20 roll of 9 or lower as a 10.

Alert literally says you have proficiency with Initiative. However, Initiative is not listed as a skill, nor is it a Tool, which is why I ask.

Initiative counted for Bard’s Jack of All Trades in 2014 because that ability says:

Starting at 2nd level, you can add half your proficiency bonus, rounded down, to any ability check you make that doesn’t already include your proficiency bonus.

Initiative is definitely an Ability Check.

The 24 Jack of All Trades is worded in a more complicated way that makes it somewhat questionable:

You can add half your Proficiency Bonus (round down) to any ability check you make that uses a skill proficiency you lack and that doesn’t otherwise use your Proficiency Bonus.

It still says “to any ability check,” but it also says “that uses a skill proficiency you lack,” does that mean it no longer works with Initiative, if Initiative does not count as a skill?