H1-B and L1 can actually be done in-country, but for some reading going abroad and get consular processing has a lower chance of RFE.
You are talking about change (or extension) of status, not visa.
US is unique in that the visa sticker and your right to remain in the country (status) are two different things. The only purpose of the visa sticker is to allow you to travel to a U.S. port of entry, where you apply for admission, and therefore legal status. You can have legal status in the U.S. while the visa sticker has expired, and your status can be changed or extended domestically. However unless you have a valid sticker you cannot leave and return.
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Based on my experience 20 years ago you could only renew the H-1B visa in the passport in-country under extraordinary circumstances. In the majority of cases they reject your request and would tell you to travel to a consulate.
Prior to the mid 00s you could renew at any consulate but they changed it so you could only renew in your home country.
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The pause on visa appointments does not apply to H1-B and L1 as they are nonimmigrant visas. It applies to family based immigration visa, diversity visa, and EB-1/2/3 when you do processing abroad.
(You might have known that, but I thought it's worth clarifying).
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