Update module github.com/pulumi/pulumi/pkg/v3 to v3.222.0 (#653)

This PR contains the following updates:

| Package | Type | Update | Change |
|---|---|---|---|
|
[github.com/pulumi/pulumi/pkg/v3](https://redirect.github.com/pulumi/pulumi)
| require | minor | `v3.221.0` -> `v3.222.0` |

---

### Release Notes

<details>
<summary>pulumi/pulumi (github.com/pulumi/pulumi/pkg/v3)</summary>

###
[`v3.222.0`](https://redirect.github.com/pulumi/pulumi/releases/tag/v3.222.0)

[Compare
Source](https://redirect.github.com/pulumi/pulumi/compare/v3.221.0...v3.222.0)

##### 3.222.0 (2026-02-18)

##### Features

-   \[programgen/go] Generate Call requests
[#&#8203;21836](https://redirect.github.com/pulumi/pulumi/pull/21836)

##### Bug Fixes

- \[sdk/{nodejs,python}] Fix hang when loading policy packs that use
v1.18.1 or older of the policy SDK
[#&#8203;21866](https://redirect.github.com/pulumi/pulumi/pull/21866)

</details>

---

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---

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---

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tests/go.mod

@@ -5,8 +5,8 @@ go 1.25.0
 replace github.com/Sirupsen/logrus => github.com/sirupsen/logrus v1.9.3
 
 require (
-	github.com/pulumi/pulumi/pkg/v3 v3.221.0
-	github.com/pulumi/pulumi/sdk/v3 v3.221.0
+	github.com/pulumi/pulumi/pkg/v3 v3.222.0
+	github.com/pulumi/pulumi/sdk/v3 v3.222.0
 	github.com/stretchr/testify v1.11.1
 )
 

tests/go.sum

@@ -357,10 +357,10 @@ github.com/pulumi/appdash v0.0.0-20231130102222-75f619a67231 h1:vkHw5I/plNdTr435
 github.com/pulumi/appdash v0.0.0-20231130102222-75f619a67231/go.mod h1:murToZ2N9hNJzewjHBgfFdXhZKjY3z5cYC1VXk+lbFE=
 github.com/pulumi/esc v0.22.0 h1:Kbk0kIPsoIu6vnLgKtiE8AKRfl8B8bg6adiQuwJiBjA=
 github.com/pulumi/esc v0.22.0/go.mod h1:mkghIFn/TvN3XnP4jmCB4U5BG1I4UjGluARi39ckrCE=
-github.com/pulumi/pulumi/pkg/v3 v3.221.0 h1:0mfTZOj5RkkOlYhFUgVdRtPX2CIQNUscjcLMQiQKshQ=
-github.com/pulumi/pulumi/pkg/v3 v3.221.0/go.mod h1:qC8yKzKvIvFG0YQ6ElETi52hC0K1xCHjDUST6ZNlkug=
-github.com/pulumi/pulumi/sdk/v3 v3.221.0 h1:2cT5HvWkfT4AV7kpVZGie9U2NI2aSxTxwjBzRd1MqKk=
-github.com/pulumi/pulumi/sdk/v3 v3.221.0/go.mod h1:UGWJOz25OiFIN0QH79UFij8mffH94TYebKUgy9Wvug0=
+github.com/pulumi/pulumi/pkg/v3 v3.222.0 h1:Om20ZsLUqKDfcm6LQg2zZnHqVP7H/iPhxe8m2ZH0Ol0=
+github.com/pulumi/pulumi/pkg/v3 v3.222.0/go.mod h1:N0lcv+SWVj41N4Me8YHLtFy2Vo4iyBMtqqSdBaV5zFg=
+github.com/pulumi/pulumi/sdk/v3 v3.222.0 h1:aHuJcnq3b339p0DhkMBN0EaQOSvojnwpbP1W1QWv8pI=
+github.com/pulumi/pulumi/sdk/v3 v3.222.0/go.mod h1:UGWJOz25OiFIN0QH79UFij8mffH94TYebKUgy9Wvug0=
 github.com/redis/go-redis/v9 v9.7.0 h1:HhLSs+B6O021gwzl+locl0zEDnyNkxMtf/Z3NNBMa9E=
 github.com/redis/go-redis/v9 v9.7.0/go.mod h1:f6zhXITC7JUJIlPEiBOTXxJgPLdZcA93GewI7inzyWw=
 github.com/rivo/uniseg v0.4.7 h1:WUdvkW8uEhrYfLC4ZzdpI2ztxP1I582+49Oc5Mq64VQ=