docs: Add stake programming documentation (#14529) (#14582)

* Add stake programming documentation

We had some questions about stake programming documentation, and there
wasn't a place that contained information about the stake-o-matic and
other stake development in one place.  This adds a page with that
information.

* Update docs/src/staking/stake-programming.md

Co-authored-by: Eric Williams <eric@solana.com>

* Update docs/src/staking/stake-programming.md

Co-authored-by: Eric Williams <eric@solana.com>

* Update docs/src/staking/stake-programming.md

Co-authored-by: Eric Williams <eric@solana.com>

* Update docs/src/staking/stake-programming.md

Co-authored-by: Eric Williams <eric@solana.com>

* Update docs/src/staking/stake-programming.md

Co-authored-by: Eric Williams <eric@solana.com>

* Apply suggestions from code review

* Remove trailing whitespace

Co-authored-by: Eric Williams <eric@solana.com>
(cherry picked from commit b37dbed479)

Co-authored-by: Jon Cinque <jon.cinque@gmail.com>

docs/sidebars.js

@@ -45,6 +45,7 @@ module.exports = {
     "Staking": [
       "staking",
       "staking/stake-accounts",
+      "staking/stake-programming",
     ],
     "Command Line": [
       "cli",