Is there a road map for those that want to employ encumbrance to put things in their inventory into containers (arrows in quivers, rations in backpack, coins in pouch).

This seems to be specifically useful for things such as portable hole and bag of holding. These would reduce your encumbrance when placing these into these items without having to manually override the weight. Also, it's  just a good way to track where things are on the character.

One curious mind would like to know.

It is moving up the list. It might be after AL support.

Is there a plan to add gems to the currency tab? This is very important for characters wishing to reduce monetary (coin) encumbrance.

Not currency, but they have already been added as items.

Gems already exist as equipment ;)

True, but equipment lists grow very long and cumbersome and gems aren't really "equipment", but rather they are currency (except in the case of ingredients for spells). Also, their presence in your equipment list doesn't add to your net worth on the currency tab.

Per RAW, gems are 'mundane treasure' rather than currency; they're broken out into their own section of the loot table from the coinage, and they're given their own sub tables.

Gems can be used as currency only in the same way that a piece of artwork can also be currency, or using ingots/bars of precious metal instead of coins, or basically anything that can be easily carried and can be traded. 

Currency is a trade of one thing of a common value used to gain something else of a common equivalent value. It's just an item to which you can attribute some form of commonly decided value.

Coins are the primary, most widely accepted, form of currency and this is why they are put separately and more prominently. Other items are not used as currency often enough to need another section specific to it - there is limited space and adding this is going to require a change in the UI. Especially since there are so many different types of gems with so many different costs and qualities. 

If you find the inventory list insufficient, then put your gems and their value in Other Possessions to make them easier to find.

Not to be argumentative, since I am really just making suggestions based on my/our play, but Webster's currency definitions aside, treasure 5e (as describe in the DM Guide random tables), has a large portion that will be in gems and other "items of value": paintings, goblets, etc. They are given specific values (not even ranges) like other common items in the game. So for in-game purposes they are essentially the same as coins or can be thought of as having a fixed value. To get around this, in our games we usually completely ignore these and just call it all "gold" unless it is too large to easily transport (i.e. - gems) or has a specific use (i.e. - magical components).

And yes, I (and I'm sure many others) put all these sorts of things in "Other Possessions" so it doesn't clutter up the "useful" inventory list.

I suppose a better solution would be to have two line items: one for value of gems and another for value of "all other items" ,so that one could see one's total available wealth in one place.

Containers and off-character storage of items is a very commonly requested and upvoted feature on the Zendesk feature requests forum. It's also something that really should've been finished in the character sheet by now as it's a huge part of inventory management. I expect it to come out some time in the next decade.

Adam actually said that inventory management and AL validation are both things that they are looking into for 2020. Here's a link to the dev update: https://youtu.be/Rjy4dAtd7xs?t=386 so fingers crossed.