Pullquote: Enable Block Bindings support

[gziolo]

Follow-up for #9702.
Backport for WordPress/gutenberg#70975. This should land only when we add Block Bindings support for Pullquote in Gutenberg.

Trac ticket: https://core.trac.wordpress.org/ticket/63919

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Props gziolo.

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[gziolo]

After talking with @mtias, I'm going to close this PR as we are going to deprecate the Pullquote block soon:

• Pullquote: Deprecate the block in favor of Quote block gutenberg#11610