Align ci/publish-docs and ci/test-checks doc builds (#9653)

* Align ci/publish-docs and ci/test-checks doc builds

* Fix links

docs/build.sh

@@ -12,5 +12,6 @@ find src -name '*.md' -a \! -name SUMMARY.md |
    fi
  done
 
-
-make -j"$(nproc)" test
+mdbook --version
+mdbook-linkcheck --version
+make -j"$(nproc)"

docs/src/clusters.md

@@ -49,7 +49,7 @@ $ solana-validator \
 * Testnet is where we stress test recent release features on a live
 cluster, particularly focused on network performance, stability and validator
 behavior.
-* [Tour de SOL](../tour-de-sol/README.md) initiative runs on Testnet, where we
+* [Tour de SOL](tour-de-sol/README.md) initiative runs on Testnet, where we
 encourage malicious behavior and attacks on the network to help us find and
 squash bugs or network vulnerabilities.
 * Testnet tokens are **not real**
@@ -89,7 +89,7 @@ Currently smart contracts, rewards, and inflation are disabled.
  * If you have paid money to purchase/be issued tokens, such as through our
  CoinList auction, these tokens will be transferred on Mainnet Beta.
    * Note: If you are using a non-command-line wallet such as
-   [Trust Wallet](../wallet/trust-wallet.md),
+   [Trust Wallet](wallet/trust-wallet.md),
    the wallet will always be connecting to Mainnet Beta.
  * Gossip entrypoint for Mainnet Beta: `mainnet-beta.solana.com:8001`
  * RPC URL for Mainnet Beta: `https://api.mainnet-beta.solana.com`

docs/src/running-validator/validator-start.md

@@ -138,7 +138,7 @@ Airdrop yourself some SOL to get started:
 solana airdrop 10
 ```
 Note that airdrops are only available on Devnet. Testnet SOL can be obtained by
-participating in the [Tour de SOL](../tour-de-sol) program.
+participating in the [Tour de SOL](../tour-de-sol/README.md) program.
 
 To view your current balance: