The section on "Longer Casting Times" states:

When you cast a spell with a casting time longer than a single action or reaction, you must spend your action each turn casting the spell...

In trying to write an answer to the question "Can you cast bonus action and reaction spells while already casting a spell" I became unsure whether spending your action maintaining a spell actually counts as casting a spell for the purposes of this and features like the following:

The Abjuration Wizard's Arcane Ward feature states:

Whenever you cast an abjuration spell of 1st level or higher, the ward regains a number of hit points equal to twice the level of the spell...

The Valor Bard's Battle Magic feature states:

When you use your action to cast a bard spell, you can make one weapon attack as a bonus action...

The Sorcerer's Elemental Affinity feature states:

Starting at 6th level, when you cast a spell that deals damage of the type associated with your draconic ancestry, add your Charisma modifier to that damage.

The Life Cleric's Blessed Healer feature states:

When you cast a spell of 1st level or higher that restores hit points to a creature other than you, you regain hit points equal to 2 + the spell's level.

The Wild Magic Sorcerer's Wild Magic Surge feature states:

Immediately after you cast a sorcerer spell of 1st level or higher, the DM can have you roll a d20.

Does this mean that Arcane Wards are healed several times, Valor Bards can make a weapon attack each turn, Sorcerer's can add their Charisma modifier multiple times to a damage roll, Life Clerics are healed multiple times, and that multiple Wild Magic Surges may occur?

In terms of the odd cases of Elemental Affinity and Blessed Healer happening multiple times I parse their paragraphs so that the spell doesn't actually have to deal damage or restore hit points, it only to be a spell that usually does those things.

This is supported in the question on "When must the wizard choose to overchannel?
" where the following is said:

The timing for using Overchannel is "when you cast", and a spell you can use it on is "a wizard spell of 5th level or lower that deals damage". This is merely meant to specify that you can only use it on spells that include damage as part of their effects (like fireball), as opposed to spells that don't deal any damage (like invisibility).

If it was meant to be decided after it had dealt damage, it would have to use wording like "When you cast a wizard spell of 5th level or lower and deal damage".

Maintaining a spell counts as casting, but you only cast a single spell. The Bard triggers his feature multiple times, and others trigger only once.

The Wild Sorcerer is the clearest of all. After you cast clearly indicates that the spell has finished casting.

Immediately after you cast a sorcerer spell

The others are not so obvious, but it seems a reasonable interpretation of the rules that they also mean when you finish casting. If the text said While you cast it would be quite the opposite.

When you cast a spell

Afterall, you would only give the ward some points if you completed the spell, not if you got counterspelled or something.

However, the bard is the exception here.

When you use your action to cast a bard spell

This is what you are doing for multiple turns, to cast the spell. Everytime you declare that your action is spent casting, then you completed the condition:

You must spend your action each turn casting the spell

So the Bard would make multiple attacks throughout the casting.