Embassies are not "foreign soil". The Russian Embassy in London, for example, is not a Russian place, it's a British place that just happens to have a Russian Embassy building on it. Russians there are not magically exempt from British law.
However, in practice diplomacy is impossible without affording Ambassadors, their staff, the places where they live and work and so on, broad immunity to normal civil law enforcement. Eventually this was formalised as the Vienna Convention, and the current iteration of that convention is the state of the art as far as relations between most countries are concerned.
As a result Convention signatories do NOT on the whole search embassies of other signatories in their country. But it's not because the embassy in any sense isn't in their country.
For example the US government absolutely could tell the Russian mission to all shove off back home, they would be entitled to a "reasonable" amount of time to leave, and then the Ambassador (if he has foolishly remained) is just a Russian citizen in the US without immigration papers, the same for all staff and families. The embassy, the homes, and other facilities are all just ordinary buildings able to be searched by police, parcels sent to the embassy become just ordinary parcels which may be opened, examined, redirected or destroyed as appropriate by the USPS. The Americans would never choose to do this, because diplomatic contact with Russia remains essential, in anything short of total war, but legally they absolutely could.