fix(esphome): Update persistence for correct cache directories (#32763)

**Description**
I figured this out when looking for why my volsync backup was so large
for what should be just a couple yaml files. This saves me 1.3GB of S3
storage, but that quantity will vary.

Now we're mounting the cache directories that esphome is expecting. If
they don't see these directories existing, then they change the location
to be inside the config directory so that these things are cached.

It looks like we used to have this working, but upstream probably
changed the directories at some point. They don't seem to have clear
documentation that I could find. I found these directories [in their
github](https://github.com/esphome/esphome/blob/dev/docker/docker_entrypoint.sh).

⚒️ Fixes  # N/A

**⚙️ Type of change**

- [ ] ⚙️ Feature/App addition
- [x] 🪛 Bugfix
- [ ] ⚠️ Breaking change (fix or feature that would cause existing
functionality to not work as expected)
- [ ] 🔃 Refactor of current code
- [ ] 📜 Documentation Changes

**🧪 How Has This Been Tested?**
Deployed locally and then updated my devices. It'll have to redownload
the packages, but there's no breaking change from what I found.

**📃 Notes:**
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**✔️ Checklist:**

- [x] ⚖️ My code follows the style guidelines of this project
- [x] 👀 I have performed a self-review of my own code
- [x] #️⃣ I have commented my code, particularly in hard-to-understand
areas
- [ ] 📄 I have made changes to the documentation
- [ ] 🧪 I have added tests to this description that prove my fix is
effective or that my feature works
- [x] ⬆️ I increased versions for any altered app according to semantic
versioning
- [x] I made sure the title starts with `feat(chart-name):`,
`fix(chart-name):`, `chore(chart-name):`, `docs(chart-name):` or
`fix(docs):`

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---------

Signed-off-by: mgale456 <55673155+mgale456@users.noreply.github.com>

charts/stable/esphome/Chart.yaml

@@ -32,4 +32,4 @@ sources:
   - https://github.com/truecharts/charts/tree/master/charts/stable/esphome
   - https://hub.docker.com/r/esphome/esphome
 type: application
-version: 22.0.1
+version: 22.0.2

charts/stable/esphome/values.yaml

@@ -43,9 +43,14 @@ persistence:
   config:
     enabled: true
     mountPath: /config
-  platformio:
+  # caches platformio packages to prevent excess downloads
+  cache:
     enabled: true
-    mountPath: /.platformio
+    mountPath: /cache
+  # caches compiled code to not require rebuilds
+  build:
+    enabled: true
+    mountPath: /build
 portal:
   open:
     enabled: true