I like the new template! Just a few minor comments:

  • You say that the abilities/spells should be "level appropriate for the binder's level" - should that be the vestige's level, (ie. roughly equivalent to a spell of that level, so a 4th-level vestige gets 4th-level spells or something of that power) or did you mean "appropriate to a binder at the level where they gain access to this vestige"? ...Actually, there's not much difference between those two, but still, worth clarifying how to determine what's "level-appropriate".
  • I like the idea of one ability that scales with the binder's level, and one that doesn't. That covers the same kind of angle I was after when I decided on having abilities at half the level as well as the full level.
  • Some vestiges (particularly higher-level ones) may need a broader spread of abilities; perhaps as well as the one or two levelled abilities, they might get one or two at half their level as well. I say this because some of the 3.5 vestiges grant up to six or seven abilities.
  • I agree with your worries about skill proficiencies, and you're right, advantage on the skill check works much better. Part of this comes from me interpreting 3.5's bonus to skill checks as a modifier, hence proficiency, forgetting that in 5e bonuses usually take the form of advantage on the roll. I might be ok with a few vestiges (and I mean at most a handful, mostly in the upper levels) granting the odd skill proficiency (never more than one per vestige) where it's really thematically appropriate.
  • This last point is more of a clarification but on the subject of abilities, where you've got "2 once-per-short-or-long-rest abilities/features" I think it's worth noting that not all of them should be once-per-short-rest except in exceptional circumstances - I don't really want a binder to be able to burn out one particular vestige and spend the rest of the day with that vestige being mostly useless. Of course, if the cantrips and proficiencies are good enough, that'll cover it, and there's always renegotiation, so for a few vestiges it'd be fine, but in general they should provide something of a little more power that remains useful all day. At low levels, cantrips are pretty powerful when your top level of spell is only 1st or 2nd, so only having once-per-long-rest features is fine, but an 8th-level vestige that you can exhaust in the first encounter and be left with cantrips for the rest of the day feels kinda wrong. Bear in mind that a binding lasts for 24 hours, so an ability that can only be used once per long rest really means once per binding in most cases.

That last point reminds me, I should probably clarify at some point whether a vestige's once-per-rest abilities reset when you re-bind them, thus allowing you to use a once-per-rest ability, expel, rebind, and use it again. In short: no, that doesn't work. Technically this is already covered because it says "you can't use this ability again until you complete a rest", but I'd still feel better if somewhere it added "...even if you bind this vestige a second time".

Could I also ask that the paragraphs of vestige information keep a clean separation between flavour and mechanics? In other words, don't bury something in there about getting advantage on the check in certain conditions or whatever. 5e does a good job of making it fairly obvious what's flavour text and what's rules, so I'd like to follow that example. I'll probably keep all mechanical stuff at the end of that section, next to the bit about the influences on a poor pact. This would also make it easier to produce quick reference cards for players by simply dropping the vestige information part and just adding the influences table.