Are there any immigration quotas or limits for Japan?

There are no quotas or limits on Japanese naturalization. In fact, there are no limits or quotas for permanent residency or other types of visas (including refugee and asylum seekers) in Japan.

There are many misunderstandings about Japan's immigration rules and polices. Superficially, people look at the small legal foreigner population — approximately 2% of the population of Japan if you include the legally non-Japanese but born and raised in Japan that are colloquially referred to as the 在日 {Zainichi} (literally, "residing in Japan", but with the nuance of Koreans born and raised in Japan).

There are many reasons for the small foreigner population in Japan, but a restriction on the number of people they let immigrate is not one of them.

It's also not true that the immigration process is difficult compared to other countries with respect to the procedures. The procedures and requirements for naturalization are very similar to many European countries such as Germany.

It is true that Japan is stricter with respect to determining who is and isn't a genuine by-the-book-definition of a refugee / asylum seeker. Other countries are far more liberal with respect to examining individual cases.

Countries like the United States have huge immigration rates because they have an immigration policy that Japan does not: the United States historically (and even today) receives the majority of their (legal) immigration through "family reunification" policies. While America's policies can apply to extended family, Japan's policies regarding the getting a visa on the basis of family already living in Japan is limited to two cases:

1. immediate family dependants (your spouse and children)
2. connection to a Japanese national up to three generations. This is how the Brazilian-Japanese population swelled in the late 80s and 90s; many Brazilians immigrated using this policy to receive a 定住者 {teijūsha} (long term resident) 在留資格 {zairyū shikaku} (foreigner Status of Residence / SoR).

The real reason that Japan's immigration numbers are low is probably due to one reason: the Japanese language. Most countries that have high naturalization / immigration rates have environments where English, the most common second language in the world, is commonly used. When the country doesn't have a large English environment, other political factors are involved. For example, Russia has a high immigration / naturalization rate due to the legacy of the Soviet Union, and people from the Warsaw nations becoming legally Russian.

Just because there is no quota or limit today or yesterday does not mean there won't ever be a quota in the future. However, so long as the Japanese language is required for general purpose economic success in Japan — excluding specialized jobs in English teaching, finance, and professional STEM jobs — it's foreseeable that the "unwritten language requirement" will naturally keep the annual immigration numbers low.