I think your putting goals are set much higher than the chipping goals.

2 putting 90% of the time from 13 meters is extremely good, and to accomplish this, I would say at a minimum, your average putt from 13 meters will have to end up less than a meter from the hole. If it were me, I would lower this goal to 2 putting 90% from 3-10 meters. That's IMO, pretty close to a scratch golfer's putting ability. Also, making 50% from 1-3 meters and 90-95% from 1 meter in would also be very excellent putting.

As for the chipping, getting a 30 meter chip to 5 meters is a so-so accomplishment. Now for a bogey golfer, this is pretty good, because you probably aren't going to 3 putt from 5 meters, but the chances of saving a stroke and getting up and down are pretty low.

Now the first thing I think a 20 something handicapper needs to accomplish is to just make sure that pretty much all chips get within comfortable 2 putting range. That can generally be accomplished by just having a consistent stroke and making consistent solid contact on every chip (not hitting the ball very fat or thin very often at all). But it doesn't sound like you are going to be satisfied with just having the chipping game of a bogey golfer (and as it sounds like you are serious about improving, and primarily the short game first, there is no reason to be satisfied with this). But that is the first thing to master IMO with chipping. Just as distance control should be learned first with putting, and later direction, I think with chipping, direction and consistent contact should be worked on first, and then more attention to distance control. What's the point of perfect distance on a well struck chip if 20% are poorly struck and many of the chips end up 5 meters off line? A chip with perfect distance 5 meters off line is no better than a chip with perfect direction that is 5 meters short or long.

So chipping goals could be structured something like this:

Goal 1: Hit 90% of chips with solid contact and within 1 meter of the intended direction.
Goal 2: Be able to get a chip on average within twice the distance you would leave an average putt from the same distance. So if your average leave on a 20 meter putt is 1.5 meters, your average leave on a 20 meter chip would be 3 meters.
Later Goals: Set a goal of some percentage of all chips getting within 2 or 3 meters. The simple truth is that no matter how good you get at putting, you are never going to make most of your putts over 3 meters. So saving strokes with chipping means getting the ball within 3 meters, or better, 2 meters.

Another thing ... until you get good with irons and wedges, you will most likely be making a chip on the majority of holes. So getting very good at chipping will likely pay greater dividends than getting very good at putting.