haswbstatement currently supports datatypes such as external identifier and string but not the URL datatype.
It would be very useful if one could search for urls in the following manner:
https://www.wikidata.org/w/api.php?action=query&list=search&srsearch=haswbstatement:P856=http://www.nationalmuseum.se/
For wikidata properties types they need to be explicitly whitelisted. I poked through our data and the field that currently holds this data has ~241M unique values. Adding the url's should only increase it by 1-2M, so probably fine. Or not entirely fine, these 241M unique values have to stay resident in memory multiple times, but adding 1% isn't going to change anything.
For actually rolling this out, it will be between 2 and 3 months after the config change is shipped for the wikidata index to be fully populated with urls
Change 577312 had a related patch set uploaded (by EBernhardson; owner: EBernhardson):
[operations/mediawiki-config@master] Whitelist urls for inclusion in wikidata statements indexed to search
Change 577312 merged by jenkins-bot:
[operations/mediawiki-config@master] Whitelist urls for inclusion in wikidata statements indexed to search
Forced a reindex on Q842858, it is now returned by the example query. As mentioned it will be two to three months before this has the urls indexed for all wikidata items.