Improved Context API docs

[its-the-shrimp]

Description

1. Added an example of how to produce context updates from a struct component
2. Updated the docs of use_context to point to the actual Yew Docs page about using contexts.
3. Synchronised examples of usage of use_context here and here

Fixes #2943, fixes #2927

Checklist

• I have reviewed my own code
• I have added tests

[github-actions]

Size Comparison

examples	master (KB)	pull request (KB)	diff (KB)	diff (%)
async_clock	102.409	102.409	0	0.000%
boids	175.650	175.650	0	0.000%
communication_child_to_parent	95.304	95.304	0	0.000%
communication_grandchild_with_grandparent	109.040	109.040	0	0.000%
communication_grandparent_to_grandchild	105.716	105.716	0	0.000%
communication_parent_to_child	92.782	92.782	0	0.000%
contexts	110.994	113.452	+2.458	+2.215%
counter	89.196	89.196	0	0.000%
counter_functional	89.932	89.932	0	0.000%
dyn_create_destroy_apps	92.369	92.369	0	0.000%
file_upload	103.526	103.526	0	0.000%
function_memory_game	174.630	174.630	0	0.000%
function_router	353.013	353.013	0	0.000%
function_todomvc	163.523	163.523	0	0.000%
futures	227.415	227.415	0	0.000%
game_of_life	112.359	112.359	0	0.000%
immutable	188.779	188.779	0	0.000%
inner_html	85.980	85.980	0	0.000%
js_callback	113.370	113.370	0	0.000%
keyed_list	201.298	201.298	0	0.000%
mount_point	89.188	89.188	0	0.000%
nested_list	114.602	114.602	0	0.000%
node_refs	96.289	96.289	0	0.000%
password_strength	1583.745	1583.745	0	0.000%
portals	98.358	98.358	0	0.000%
router	319.013	319.013	0	0.000%
simple_ssr	144.150	144.150	0	0.000%
ssr_router	390.805	390.805	0	0.000%
suspense	118.896	118.896	0	0.000%
timer	91.795	91.795	0	0.000%
timer_functional	100.468	100.468	0	0.000%
todomvc	143.679	143.679	0	0.000%
two_apps	89.896	89.896	0	0.000%
web_worker_fib	138.875	138.875	0	0.000%
web_worker_prime	190.399	190.399	0	0.000%
webgl	88.553	88.553	0	0.000%

⚠️ The following example has changed its size significantly:

examples	master (KB)	pull request (KB)	diff (KB)	diff (%)
contexts	110.994	113.452	+2.458	+2.215%

[github-actions]

Visit the preview URL for this PR (updated for commit 2fb5d4c):

https://yew-rs--pr3409-fix-context-api-docs-iyn2cc5p.web.app

_{(expires Sat, 30 Sep 2023 11:59:53 GMT)}

_{🔥 via Firebase Hosting GitHub Action 🌎}

[github-actions]

Benchmark - SSR

Yew Master

Benchmark	Round	Min (ms)	Max (ms)	Mean (ms)	Standard Deviation
Baseline	10	422.911	424.146	423.365	0.437
Hello World	10	779.589	780.474	780.005	0.326
Function Router	10	2505.927	2527.189	2515.800	6.680
Concurrent Task	10	1008.666	1011.097	1010.296	0.741
Many Providers	10	1792.772	1825.000	1803.041	10.036

Pull Request

Benchmark	Round	Min (ms)	Max (ms)	Mean (ms)	Standard Deviation
Baseline	10	422.941	424.557	423.978	0.481
Hello World	10	779.381	786.896	781.507	2.845
Function Router	10	2505.288	2519.078	2512.981	4.757
Concurrent Task	10	1008.970	1014.338	1010.922	1.445
Many Providers	10	1770.582	1813.011	1780.058	12.755

[ranile]

Thank you very much for PR!

[cecton]

Lot of minor comments but LGTM

[cecton]

(Unnecessary white space added. Really not important)

[cecton]

Doesn't this one have the same issue than #3396?

[cecton]

Should probably use AttrValue 😁

[cecton]

Either it's the first sentence (one line) or it's a new paragraph, in which case we need spacing

Suggested change

	/// The toolbar.
	/// This component has access to the context
	/// The toolbar.
	///
	/// This component has access to the context.

Suggested change

	/// The toolbar.
	/// This component has access to the context
	/// The toolbar. This component has access to the context.

[cecton]

Suggested change

	/// Button placed in `Toolbar`.
	/// As this component is a child of `ThemeContextProvider` in the component tree, it also has access
	/// to the context.
	/// Button placed in `Toolbar`.
	///
	/// As this component is a child of `ThemeContextProvider` in the component tree, it also has access
	/// to the context.